Tactics trainer, Chess mentor, online tournaments
Most Useful Feature

I came for the e-chess (incl. tournaments), I paid for the Chess Mentor, and I stay for the Tactics Trainer. :)
Seriously, those three are tops for me.
Game Explorer is huge too, but I won't use that significantly till it's integrated with e-chess. As it stands now, I've got an e-chess interface that shows me the FEN for the current position and a Game Explorer that can't take FEN as an input. The upshot is that the FEN is really just an invitation to go to a different website and look it up, if you're studying opening lines...
(Sorry, slipped into constructive criticism mode there...)
Best site ever!

Chess Mentor and Tactics Trainer. I really like Chess Mentor, but didn't like that it was timed (my membership came with 8 hours of Chess Mentor) -- I may go Diamond when my Plantinum membership runs out now that it included Chess Mentor.
I think the Computer Workout has potential, but I haven't quite figured out how best to use it.

On-line tournaments and live chess. I "study" (actually do some theory and analysis) at the chess club on Wednesdays, otherwise I prefer to learn by playing or try out my new skills in practice. Tournaments are great, but very time demanding, and it's rude to take a vaction. Live chess has the advantage of being able to finish the game in one sitting.
What feature on chess.com is your favorite? I am making a survey here just for curiosity. These are the features I would like to test.
Articles
Chess Mentor
Blogs
Live Chess
Computer Workout
Tactics Trainer
Game Explorer
Online Tournaments
Other