It is one thing to break down a historical model, it is something else to replace it by something better. Here is my try.
When discussing top players, it is generally useless to try to bind them to one specific style. But that does not mean, that distinguishing styles must be abandoned totally. It is only natural, that the strongest players keep on developing their play. They will continue incorporating new ideas - or cease to be a top player.
Take for instance Adolf Anderssen. Before his lost match against Morphy one might say, he played old fashioned coffee-house chess. After the match his tactical attacking play was much more based on Morphy's positional principles of open positions.
Or take Lasker. Much is already said about his play before 1914. But even after 1921 he remained a top player - with a much more classical/technical style.

In this respect it is interesting, to compare Spielmann-Nimzovitsj, Semmering 1926, with Nimzovitsj-Spielmann, Karlsbad 1929. Both games were decisive for the tournament victory. In Semmering the game became very dynamic in an early stage. Spielmann proved to be better in this type of position. In Karlsbad Spielmann's dynamic (maybe forcing is better) style was confronted with Nimzovitsj hypermodern ideas. The latter won, as Spielmann did not get enough dynamic compensation for the structural weaknesses he accepted in the opening. This is in my opinion the best game Nimzo ever played, better than the famous ones against Johner and Sämisch.

So when distinguishing styles, we should apply them merely on games, not on players. Then it is easy to see, that the aggressive Kasparov has won many fine "dry" technical games and that the defender Karpov has won as many fine attacking games.

When periodizing chess history, we must look at two aspects: which style was most often applied and which style had most success.
From 1919 until 1927 we can distinguish three styles: the technical/classical, the hypermodern and the forcing style. A famous example of the latter is Bogoljubow-Alekhine, Hastings 1922 (or was it 1923?). In 1927 Alekhine completely adopted the technical/classical style, to beat Capa on his own territory. As Alekhine withdrew from tournament play, three transition years followed. Alekhine came back in 1930 and changed the scene forever, treating his former equals as beginners.
This is why I state, that the classical era lasted until 1927. But even in Capa's and Spielmann's play we can recognize the influence of the hypermoderns. The first adopted the Queen's Indian and the latter played several games with Benoni structures. Of course both interpreted hypermodernism in their own way.

From 1970 and further I do not really see one specific style prevail. All topplayers - including Fischer - had become universal. What they do, is improving themselves on every aspect of the game. An intriguing question is, when the limit will be reached.

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That's exactly my problem. You can take any part of a style (in this case a scientific approach) and use it to support a trend. I can just as easily use Lasker's match against Schlechter (5-5) to illustrate his non-scientific adventurism: The first 4 games were drawn as Lasker couldnt go through Schlechter's defensive setup. Then the 5th game he got fed up and decided to make it interesting, he lost. Than 4 draws and then in the last game he uses the psychologically only available tool, that is to have Schlechter choose between a drawish or a winning continuation. Lasker won that game eventually after he should have lost a couple of times. 
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Not disagreeing with you about Tal, just that he fits in a "soviet school" definition. Imo that style is purely professional, so based on efficiently beating weaker players and not running into too much risk against equals. On the other hand I find it hard to define a school on that basis. As an example of my problem. Check all the matches Botwinnik lost. Smyslov beat him with a very Petrosjan-like approach, Tal shell shocked him and Petrosjan prophylaxed him (for lack of a better word). I think you woud agree with me that Portisch and Szabo were more "soviet-school" than those examples. What I think is more usefull is to talk about soviet dominance in chess. All their grandmasters got a salary and werent allowed to ask for high pricemoney. This meant every tournament director in the west could easily get a few of the best communist players, while for western players it was far less interesting to remain professional. During those days many promising talents in the west switched to more profitable or secure occupations. All that said, I cant find one single soviet school, it is just way too diverse, though you may be able to group it according to location, ie a Baltic school, Leningrad school etc.

I like the ability of historians to build beautiful theories. But sometimes I wonder, if they check them with practical evidence? HgMan and Willempie already have cast doubt on the socalled dynamic Sovjet school. I will try to do the same on the twenties, the highlight of  hypermodernism. Who were they?
Among the topplayers I cannot think of more than three: Réti, Nimzowitsj and Tartakower. Breyer also had a hypermodern style, but he never reached the top.
Breyer won Berlin 1920, but only two games can be called hypermodern.
Réti won Stockholm 1920 and Teplice-Sanov 1922, but not with typical hypermodern chess.
Tartakower won London 1927, but again not only with hypermodern chess.
Remains Nimzovitsj, who won three or four main events in his famous style.

What about the non-hypermodern players?
Lasker won Moravska Ostrava 1923 and New York 1924.
Capablanca won London 1922, New York 1927 and Berlin 1928.
In the two WCh matches we will not find any hypermodern play.
Alekhine won Karlovy Vary 1923 and Baden Baden 1925. Hardly a trace of hypermodern chess here.
Bogoljubow won Bad Pistyan 1922, DSB-Kongress 1925, Moscow 1925 and Bad Kissingen 1928.
Spielmann won Stockholm 1919, Teplice-Sanov 1922 and Semmering 1926.

Alekhine might be influenced by hypermodernism to some extent, but in the big tournaments of San Remo 1930, Bled 1931 and Zürich 1934 we find only few games of Alekhine playing according to hypermodern principles.

So based on practical evidence I state: the Hypermodern Era does not exist. Surely there has been a hypermodern school, but it never dominated chess.
Richard Fauber: "Since much of its novelty was the opening, it got much more attention than it would have in the middle game."

In my opinion the Classical Era lasted until 1927. For the period 1927 - 1940 we must find another name, as Alekhine, Euwe, young Keres and Fine sought new ways to complicate the game.

@Willempie, 

Thank you for your considered remarks, and yes the main flaw with trying to make a general statement about periodization is the individual cases that make chess (and history) so interesting.  However, your two examples, Lasker and Tal, are actually supportive of my thesis,

Emmanuel Lasker prided himself on being a  Philosopher.  His non-chess writings are scientific, and in chess, he used the positivistic notions of psychology to augment his understanding of chess.  In a very real sense, Lasker fits very well within the Scientific Tradition of chess that Steinitz started.  Remember, the very term "steinitzian retreat" can equally be applied to the games of Lasker.  Hannak has written an interesting hagiography (worshipful biography) of Lasker which highlights Lasker's scientific approach to chess.

The 1960s were a time of tremendous social change, and chess reflects those controversial times.  However, Mikhail Tal was actually a product of the 1950s.  He benefitted greatly from the Soviet chess machine, as his "Life and Games" amply discusses.  He had access to some of the finest trainers in the world, and the Soviet Union strongly supported his bid to become a GM.  (So strongly in fact, that they allowed Larry Evans of the US to become a GM as "an exchange of hostages" as Tal describes it.)  The Soviet Union also helped Tal to challenge for the right to play in the World Championship, despite concerns that his sacrifices were ultimately unsound.   

Stylistically, Tal's game fits very well within the dynamic school of chess.  One of the great quotes about Tal went something like... "If Spassky sacrifices a pawn against you, you may as well resign, but if Tal sacrifices a pawn, keep playing, because he may then sacrifice a piece, and then who knows what will happen?"  (I believe this is a direct quote, and I think it was from Geller.)  Tal's game was directly inspired by the games of his idol, David Bronstein, and influenced the play of  many others both inside and outside of the USSR.  Bronstein also described Tal's play (again quoting from memory, so it may be off), "Tal's style is very simple to understand, first he develops his pieces in the center, then he sacrifices them somewhere.

While we remember Tal's sacrifices, it was his endgame technique that helped him to qualify for, and win the World championship.  He defeated Smyslov in a B vs N ending that wasn't clear at all, and he proved to be Botvinnik's equal or better in many of the endgames in the first match.   That technique was refined in the Soviet school.

Some interesting books on the subject include Reti's "Masters of the Chess Board", Euwe's "The Development of Chess Style", Watson's works, and Kasparov's four (and counting) volumes.   

In art, we can tell the differences between a Monet and Renoir or Seurat.  However, we can still comfortably lump them together because of their even more obvious commonalities.  Chess works in much the same way.

This really is getting interesting.

In 1992 I had one of the highlights of my career.  I gave a four-part lecture series at the United States Air Force Academy which combined two of my greatest passions, chess and history.  For my efforts, I received a nice stipend and an even better letter of thanks from the Academy. 8)

My basic thesis was that modern (around 1850-present) chess development has mirrored the changes in culture in the Industrial and Post-Industrial Age.  I explained why historians like to create periods, and how, despite their being artificial, these periods are useful for understanding general trends.  My main audience was chess players, but students of history also attended.

I broke the development of modern chess history into the following segments:


(All periods are approximations, and yes, there is overlap)

I.   The Romantics (Morphy to Steinitz)
II.  The Scientific, or Modern Era (Steinitz-Lasker)
III. The Classical School (Rubinstein-Capablanca)
IV.  The Hypermodern Era (Nimzovich-Alekhin)
V.   The Soviet School (dynamic chess) (WWII to 1960s)
VI.  The Neo-classical school (a.k.a The Fischer Era)
VII  The Age of Professional Chess (The Karpov Era)
VIII Neo-Romantic Chess (Kasparov)
IX:  The Age of Computer Chess. 

(I actually had the foresight to pick out Vladimir Kramnik as the poster child for this era that we are still in)   

I  tried to show that society creates culture, and Kasparov's chess style could not have been anticipated by the Hypermoderns any more than a Paul Morphy could somehow be transplanted to our time and be expected to rise above a normal GM level.  It isn't just a matter of learning openings, the entire culture of chess has changed.   

I argued that today is the Golden Age of Chess, and in a generation or so, Chess will either have to go through a radical change or it will be superceded in popular culture by other activities.  Young and talented players will begin to realise that they will never be as good as the best computers and find other ways to challenge themselves intellectually.

One of my unstated conceits included using very similar openings over time to show how they had been interpreted.  So for example, I demonstrated Botvinnik-Capablanca 1938 as the triumph of the Dynamic school, and used Nimzo-Indian set-ups to represent the best play of several other eras.

I also hinted that the main engine for change was the way great chess players constantly challenge the basic tenets of the era.  An example of this is that the West challenged the Soviet School's collectivism with individual brilliance.  I am not sure whether I still agree with this.

By the way, I do agree completely with John Watson's own thesis about how much chess style has changed since the Hypermoderns.

Since this is getting long, I'll stop here, and see if anyone wants me to explain myself (for example why I consider Kasparov  a "neo-Romantic" or what I mean by "Neo-classical", or to give some examples of how chess is an integral part of our culture).

HgMan's description of the historical context is very enlightening. But we should realize, that it is only true for Western culture. World War I did not have such an impact on Latin America, Africa and Asia.
If someone wants to contradict this by pointing out the rise of anti-colonial movements, then my reply is that Latin America was already independent for about 100 years and that for Asia the Japanese fleet beating the Russians in 1905 was far more important.
This obviously has nothing to do with chess-style. So in fact HgMan's arguments are confirmed, as chess around 1914 was almost exclusively a European-North American business.
Finally I must note, that Smyslov_fan did not give his own definitions of a classical versus modern style. He only tried to figure out what Spassky meant. I must say, that I am still not sure of this. When looking at the openings of the 1969, to some extent the usual definitions might apply.

This is becoming a fascinating thread, and one that might benefit from a little more historical context.  Keep in mind that the modern or anti-classical chess movement developed in tandem with the rise of a much larger modern world around World War I.  For me, the legitimate birth of modern chess was at Mannheim in 1914 (though, of course, many of its ideas had already been hatched), where some of the greatest players of the time found themselves trapped at the outbreak of war and spent their time working on the principles of what would become the modern and the hyper-modern approaches to chess.  It is no accident that this movement was not exclusive to chess.  During this same period, jazz was becoming increasingly popular: a musical genre that sought to "bend" the rules of classical music theory.  Science and technology were embraced in favor of religion and tradition, though, obviously, this conflict is ongoing--indeed, the modernist movement never replaced the older traditions, but rather sought to turn them on their heads.  It bred contentiousness rather than revolution, though sure enough we might attribute the Russian Revolution to some of these principles.  Remember that World War I was like nothing that had come before it, and it did, to an extent, turn the word upside down.  It altered the world-view of many generations to the point where the young generation of the 1920s became known as the lost generation, and produced (particularly, though not exclusively, in the United States) a new and powerful, introspective literature.  That generation rebelled against its parents and sought to live a more carefree lifestyle, bending rules and social mores.  I'm leaving a number of loose threads here and citing only a very few examples, but I hope it's sufficient to suggest that the development of modern chess did not occur in isolation, but rather as part of a much bigger and international movement of sorts.

Returning to chess, I like TalJechin's definition, but I would be inclined to want to slip in an assertion that modern chess was developed in line with the times.  But as MNb pointed out, Karpov's rejection of style is a proto-typical modern response.  These modern concepts--be it in chess, politics, literature, or music--were built less on a coherent set of rules than on a deliberate rejection of what came before them...

I thought the ideals behind the labels would be more enlightening. The belief in a 'best move' is more than just playing the best moves. Another perhaps better wording could be: the classical plays the board and the non-classical the opponent.

Your definition "a style that favors straight-forward development, a preference for "clean lines" over chaotic ones, and activity over defense." 

does seem too wide for for my taste, as it seems almost all inclusive, and not much more defined than 'classical' is from the beginning. 

'straight-forward development' is favoured by most GMs I think or it is simply theory.

'clean lines' depends a lot on one's subjective opinion and playing strength.

'activity over defense' is also an extremely common value nowadays, at least for those who want to win their games. And I don't think Petrosian's or Andersson's defensive inclination is typical of non-classical play.

But I would say that Petrosian was more interested in playing the man than the board. For example: He was very fond of delaying critical moves until move 39, so the opponent would have limited time for a crucial decision. 

And one of the ugliest wins I've ever seen was Olafsson-Petrosian in an odd Winawer. Petrosian castles q-side and then heap all pieces on the k-side, something like: Rh8,Qg8,Rf8 pawns h7,g7,f7,e6, and Ng6,Nh6... which tempts white to sac a piece on a6, but black snuffs out all compensation by just returning the pieces to the queenside with Rd8, Qe8 etc. 

The latter could be described as 'defence over activity' or non straightforward development - but I think the reason why is more enlightening than just describing what it looks like. I can't believe that anyone would advocate passivity or slow development in itself - at least not someone on the GM level which I hope we're talking about.

And playing the opponent rather than the board can be done in many ways, so Tal and Petrosian would both be non-classicals, while Kasparov and Fischer more classical in the sense of playing the board - though they had some additional ideas of how to psych their opponents when away from the board...