I'm trying to improve my game by doing some study of famous GMs and some of their best games, to try to grasp some understanding why the best chess players do what they do and how they think during their games. What's the best way to go about this? and what are some of the best/most important GMs to study?

I would recommend have a look at self annotated games. Even the video lessons here on chess.com where they annotate their own games are excellent, be sure to also check out the live sessions videos here on chess.com. It's begs to hear it from the horses mouth rather than beating your head trying to figure out for yourself those mysterious rook moves

Jose Raul Capablanca. If you play through 20 of his games, you'll jump to 1500!

in my tiny opinion

[COMMENT DELETED]

I went over karpov's entire career that was in my database one month. I just played through the games using the auto play feature in the chess base interface. After doing this I began to develop a feel for the positions and natural moves started to scream out to me. It depends on your level really, I would personally recommend a gm with a solid and positional style if your quite new to the game. Karpov is great for that, as is petrosian and nimzowitsch. They also played simple openings most of the time in comparison to the semi Slav madness you will come across from trying to figure out Kasparov

I'd recommend:

http://www.amazon.com/Mammoth-Worlds-Greatest-Chess-Games/dp/B001EEH8RE/ref=sr_1_5?ie=UTF8&s=books&qid=1277697855&sr=8-5

It's a cheap book and has many, many games to keep you occupied.

It's hard to pick a bad GM to study, actually.

---

Grandmaster Flash?

Estragon -- I was thinking the same thing myself, lol

JG27Pyth -- YES, you win.