I've not listened to remixes for long but here are my favorites:

600 A.D. in Piano - From Chrono Trigger (SNES), originally 'Wind Scene'
Note: Extremely moving piano piece.

Ascension to Cosmo Canyon - From Final Fantasy VII (PS1), originally 'Cosmo Canyon'
Note: I didn't initially like this piece, but starting at 2:26 it completely takes off and becomes absolutely amazing until the very end.

The Final Stage - From Morrowing (PC, XB), originally 'Call Of Magic' (or simply the main theme)
Note: Talk about epic. And then those bagpipes (?) at 00:42. Wow.

Anything by kLuTz (author of the first piece). I have four of his works, which is all that there is as far as I know (except for one collaboration piece with Freemind who, in his own rite, is a very accomplished pianist).

The first one was very nice, but not THAT great. I would hardly call it "extremely moving."

Frank Klepacki is the only one I know, and only because I have the C&C Tiberium Sun Soundtrack.

Edit: Blah, I just saw "Remix" in the title. Nevermind.

Klepacki isn't exactly a remixer, even though he has remixed his own songs sometimes.

I've never had patience/time/something to listen to game remixes, I tend to make silly covers myself or just listen the real thing.

So you just read "Favorite Video Game?"

Renegade of Phunk - Son of the Suns (Blues)
Renegade of Phunk - The Imperial March (Techno)
The themes for Movie Battles II. Kick *** in a way that's hard to describe. Technically not remixes, I know.

Nobou Uemetsu - A One Wingèd Angel (Advent)
Technically not a remix again, I know, but it's cool anyways.

-And even though I've only played a few minutes of the demo, the Battlefield 2 version of the Battlefield Theme is pretty cool.

Terra in Black

I dunno. I haven't visited OC Remix in quite a while.

Actually I've been making my own remixes I guess. It's fun to actually create something instead of just listening in awe to what others make.

That first remix just made me realize how much the Chrono Trigger music resembled that of Joe Hisaishi (the composer for Miyazaki's films). His music is awesome.