I remember leko saying he switched from the gruenfeld to the nimzo/nid, because it's less drawish.
I also read in Nunn's Chess Openings that the gruenfeld is not a good defence for a club player, because it's drawish and has a great amount of theory.

Thanks, these are all good recommendations. Keep them coming. 

The funny thing is that I noticed Shirov calling the Grunfeld a "very solid" defense in his DVD. What? I mean even compared to openings like the NID or QID, the Grunfeld appears far less clear or solid (correct me if I'm wrong). Does he mean solid in the sense that draws are more likely due to piece exchanges (Nxd5-Nxc3)? I understand the Grunfeld is sound but soundness and solidity are not the same thing. The Najdorf is sound too but it isn't solid like a Caro-Kann. However, it didn't seem like Shirov was confusing terms based on the context. I am a bit confused to say the least.

All of these are good choices but they require Black to be cramped for some time, much like defending the Spanish game. The advantage of the Caro-Kann and Petroff is that Black gets free development for his pieces. 

To the end, I recommend the Queen's Gambit Accepted - surely the best balance of safety and activity against 1.d4

The Slav with an early ...dxc4 is a tough nut to crack and has lots of good analysis here on ChessPub (as well as the Vigus book).  Also, you can basically learn to play that ...d5, ...c6, and ...e6 wedge against almost setup white throws at you.  Pretty handy.

Lasker's Defense in the QGD is very solid but yields few winning chances; that's why I switched to the Tartakower.  However, you can often hold Lasker's against opponents who are much stronger than you (such as computers).  But you'll need good endgame technique and enough patience to hold a slightly worse position sometimes.  

So, maybe its not exciting, but getting that half-point against someone rated 300 points higher is not such a bad thing.  And playing Lasker's might be a good way to get over theory and learn endgame play since White often has to head into the endgame to get any real winning chances.  (Your king is usually very safe.) Take a look at Yusupov's games against Karpov as well as Kramnik's games against Fritz and Kasparov.

slav with dxc4, QGD, Nimzo/QID/Catalan, Czech Benoni, Dutch Stonewall

When one just wants a safe and solid position against e4, there are always openings like the Petroff and Caro-Kann. However, I'm not so sure what the analogues are for d4 (or 1. c4 and 1. Nf3). The Slav with an early dxc4 or QGD both seem to be pretty solid. Any more ideas or comments are very welcome.