Nice! can anyone make a similar extract from 2010+ to see a possible shift in trends?
regarding OP question about which d-pawn opening for Black fits most the anti and flank systems, there is no universal answer. If you play 1.d4 Nf6, you must have something against the Tromp, same after 1.d4 d5 2.Bf4.Usually Black players pick up a main opening against d4, and adjust angainst the rest. Again, it's often better to have dedicated answers  to anti and flank openings. A great book in this respect is the BUCO by Richard Palliser (no ad intended):
Beating Unusual Chess Openings: Dealing With The English, Réti, King's Indian Attack And Other Annoying Systems (Everyman Chess) Paperback – Illustrated, February 1, 2007
by Richard Palliser (Author)
as OP seems to like "universal" openings, some popular combos are:
- French + Tarrasch (enough for 2300+ IRL)
- French + Nimzo/QID (will drive you to GM level)
- French + Dutch (1.d4 e6)
- Sicilan + KID (dark-square vs white-square openings = activity vs control)
- Sicilian + 1.c4 c5 + 1.Nf3 c5 (often: + Benoni or Dutch)
the QGD is a huge complex (currently the Ragozin is in good shape), the QGA has the merit of avoiding exchange lines but it can be dull (e.g. Nf3 lines with a4). The Tarrasch is an ideal opening to start tournaments (two modern lines: the dxc5 ending and the Dubov with Bc5) and can be upgraded with Nimzo/QID/Ragozin/Catalan. The Dutch gives home advantage to Black, but you have to like the positions (trending: the Leningrad and the Nc6 Stonewall). The KID is truly universal, but it's a chess continent of its own.
@OP: play serious/IRL games if you can, to leave broad generalities behind. When you have concrete questions  derived from experience, more people will be glad to help

Quote:

Wow, posting this comment must be the secret dream of every true grammar Nazi!
Regarding the ranking by popularity performed by OP, I'm a bit suprised to see #1: the Nimzo. Looks like many titled now play the Catalan rather than allowing the Nimzo, and 1.Nf3 against Grunfelders. 

Just curious,

But are you asking as white (what are the "best" black defenses of the d-pawn special variety you might have to face), or as black (if I chose to confront 1.d4 with a d-pawn special which one ought I to chose)? IOW, how to play them or how to beat them? Perhaps it does not matter, but I know it is pretty common for chess opening authors to write from one perspective or the other. That could affect the learning material available.

Yes, I am indeed using math symbols for comparative purposes. On the internet, this is very common, many people do that.

A = B means A is equal to B
A > B means A is slightly better than B
A >> B means A is much better than B
A >>> B means A is much much better than B
(in terms of soundness)

Nimzo > Grunfeld = Semi-Slav = QGD = QID > QGA = ...Bf5 Slav = ...a6 Slav >> Slav Schlechter = KID >>> Benko Gambit > Modern Benoni

Translation:
Nimzo is slightly better than Grunfeld.
Grunfeld, Semi-Slav, QGD, QID, all four are equal.
These four are slightly better than the QGA.
QGA, ...Bf5 Slav, ...a6 Slav, all three are equal.
These three are much better than Slav Schlechter.
Slav Schlechter is equal to KID.
These two are much much better than the Benko Gambit.
The Benko Gambit is slightly better than the Modern Benoni.

I quickly made this ranking by checking in a database of GM games and by assuming that objective goodness is proportional to popularity (the number of games in the database). It might not be perfectly accurate. It's just an approximation.

At the GM level, d-Pawn Specials are rare, so the best defenses against 1.d4 are the following (from best to worst):
Nimzo > Grunfeld = Semi-Slav = QGD = QID > QGA = ...Bf5 Slav = ...a6 Slav >> Slav Schlechter = KID >>> Benko Gambit > Modern Benoni
(based on popularity at the GM level)

What are the best defenses at lower levels, where d-Pawn Specials are much more common? What are the best defenses against d-Pawn Specials?

If White plays d4 without c4, then Black has two ways to exploit White's passivity:
- Black can gain space on the Queenside by playing ...d5, ...e6, ...c5, ...Nc6, ...Nf6. This Black setup is the QGD Tarrasch.
- Black can play ...Bf5, developping his Queen's Bishop outside the Pawn chain. Black won't need to lose a tempo by playing ...c7-c6 like he usually does when White plays both d4 and c4. Black will be able to play ...c5 in one single move instead of two. So it's an improved ...Bf5 Slav, it's a ...Bf5 Slav where Black has an extra tempo.

Therefore I conclude that at lower levels, where d-Pawn specials are much more common, the QGD and the ...Bf5 Slav are superior to all the other defenses against 1.d4.

Of course the Grammar Nazis will point out that if White doesn't play c4 it should no longer be called "Queen's Gambit Declined", and if Black doesn't play ...c6 it should no longer be called "Slav". But what you call something doesn't matter. I still call them "QGD" and "Slav" because I'm using these words to refer to two Black systems or setups. For me, the name "QGD" refers to the Black system or setup where he plays ...d5, ...e6, ...Nf6, in some order, and locks his Queen's Bishop inside the Pawn chain. For me, the name "...Bf5 Slav" refers to the Black system or setup where he plays ...d5, ...Nf6, ...Bf5, ...e6, in some order, and most often Black will also need to play ...c6 to make that work, but if White doesn't play c4 then Black won't need to play ...c6 but fundamentally it will remain the same system, the same setup.

If White plays d4 without c4, then the move ...c7-c6 would be completely useless, a perfect waste of a tempo, so the Semi-Slav setup would be stupid.