Oh man, where to start... ^^;
Of course I have to recommend just about any of the Final Fantasy OST's, though I personally loved the entirety of Final Fantasy VIII's OST. Tons of great stuff on there: "Eyes On Me," "Ride On," "Ukulele de Chocobo," "The Extreme," "Maybe I'm A Lion," "The Legendary Beast," "The Oath," "Breezy,"... The list goes on for quite a while. Oh, and of course, I have to recommend the Advent Children OST. It's got some great orchestrated pieces, as well as some awesome rock tracks, with the help of The Black Mages.
Speaking of The Black Mages, they do some nifty remixes of Uematsu's work in the Final Fantasy series. They've got two albums out so far, and are working on a third, from what I hear.
Yoko Shimomura seems to be getting most credit for the Kingdom Hearts games, though I first heard of her from Parasite Eve, most notably, the orchestral version of the main theme (entitled "Main Theme [Orchestral Version]"). Actually, to be honest, I'm not a huge fan of the KH soundtracks, but there are a handful of nice tracks. I have to strongly recommend checking out at least that one track from Parasite Eve, though. I like a handful of other tracks from the OST, but no titles really stick out right now, other than that one.
Akira Yamaoka, as mentioned previously, does the Silent Hill soundtracks' tunes. The first Silent Hill OST has mostly creepy ambient stuff, along with what can only be called "noise," haha. "Fear Of The Dark" is one of my favorite creepy tracks from it. Silent Hill 2's OST started to use some more ambient music, and even included some rock-oriented tracks, like "Angel's Thanatos." Silent Hill 3 had an overall great soundtrack, really focusing on getting more "actual" music in the game, though still incorporating that horrifying atmosphere in some tracks. It was also the first of the soundtracks to have vocal tracks, notably, "Letter (From The Lost Days)" (sung by Mary Elizabeth McGlynn, credited as "Melissa Williamson") and "Rain Of Brass Petals [Three Voices Edit]" (done by Interlace). Joe Romersa also did vocals for the ending theme, "Hometown," a remix of the original Silent Hill theme. Silent Hill 4 continued to use the usual themes, mixing the scary atmosphere of the game, some emotional instrumentation, some ambient tracks, and some rock-oriented tracks as well, featuring more vocals by Mary Elizabeth McGlynn ("Room Of Angel" and "Tender Sugar" are the two I have to point out here) and Joe Romersa.
The Suikoden games, as mentioned a few times, also have some great music. Most of anything notable about them has already been said. ^^; A variety of composers do the tunes for the Suikoden series, including Miki Higashino, Norikazu Miura, Naoyuki Sato, and others.
The Guilty Gear games have some awesome rock tracks, composed by Hiroshi Seiyama and Daisuke Ishiwatari. The one that sticks out in my mind the most is Dizzy's theme, "Awe Of She."
The F-Zero games also have some awesome music; some techno/synth-oriented, some rock, and similar sounds. "Mute City" and "Big Blue" are generally the two more well known tracks. (I have to fully agree that "Big Blue" is amazing.)
I have to join the others in backing up Yasunori Mitsuda, for the wonderful soundtrack for Chrono Trigger. Good stuff.
Also, there were several attempts by fans to remake Chrono Trigger, but this one project in particular, Chrono Resurrection, left behind a few of their redone tracks from the game. (Found at the bottom of this page:
Clicky.)
(On another note related to CT, OCRemix had a project based on the music of CT, known as "Chrono Symphonic," featuring remixes of several tracks from the game, aiming for a movie-like sound.)
Mario 64 had some great tunes, though I don't know the name of the composer(s) behind the soundtrack. "Jolly Roger Bay" is a personal favorite.
While I'm bringing up Nintendo games here, the good ol' Donkey Kong Country games actually had some amazing soundtracks. All sorts of sounds mixed in there, based on the different areas of the games that they're played during. (If you're into OCRemix, check out their "Kong In Conert" project.)
Harry Gregson Williams did some amazing scores for the Metal Gear series, and I believe he even won an award or two for it. Definitely check out his stuff.
I'm not sure who composes the music for them, but the Castlevania games have some good music as well. The only one I can personally point out, though, is Symphony Of The Night. "The Tragic Prince" has always been a favorite of mine.
Koji Kondo does some great work for the Legend Of Zelda games, particularly Ocarina Of Time and Majora's Mask. (I haven't played others, so I can't say much about them.)
From what I recall, Lunar: Silver Star Story also had a great soundtrack. I'd imagine Lunar 2: Eternal Blue had one of similar quality.
The Wild Arms series has some interesting music. It's generally a nice blend of orchestral instrumentation and a "Wild West" sort of sound.
Aside from the usual soundtracks, I also have to agree that a lot of stuff on OverClocked Remix is wonderfully done. Ailsean's "Terra In Black" is one of the notorious tracks on there. Another one I really love is Sefiros' "Everything = Nothing," a remix of "Compression Of Time," from Final Fantasy VIII. Tons of great stuff on there. VGMix also has some good stuff.
I'm sure I'm missing plenty, but I guess that's a long enough list for now anyway. ^^; Hope I was some help.