Well, since it hasn't been mentioned yet, I have to say the sound track to "Soul Bringer" -- it really set the mood and I can hear it still. Loved it.
Also, the music sound track(s) to the 3DO version of "Road Rash" were great.

Forgot how amazing the Ecco the Dolphin OST is.

My absolute favourites are Command & Conquer and Red Alert (1). I'm also very fond of the Grand Theft Auto: Vice City, Half-Life series and Michael Jackson's Moonwalker soundtracks.

I ain't got 5 up my sleeve but concerning GOG.com games I own, I must say:
Beyond Good And Evil's : pro-pa-gan-da (or whatever it's called)
is pretty damn good and catchy, I always have to sing it when I play(ed) the game.

Hmm... I'd say, in no particular order:
Final Fantasy in general, VII in specific
Planescape: Torment
Mass Effect
Braid
Well, that's only four, but they're the ones that really stick out. I can't really recall the Banjo-Kazooie music off-hand, although I recall being very fond of it back then.
HoMM3 or HoMM4 might get a spot, but it's been a while since I played those games. I do know I loved the HoMM4 vanilla title screen music despite the looping bug...
I'm also a big fan of Jeremy Soule, for obvious reasons.
World of WarCraft deserves an honourable mention at the very least, especially the music from the expansion packs. My favourite track would be... aww, I can't pick one. I gues it's between Ulduar and Grizzly Hills. Actually, Blizzard makes awesome music for their games. Unfortunately the music tends to be overshadowed by the polished gameplay when one looks back on their games.
Let's see, what's left...? Everyday Shooter is a very impressive accomplishment, and enjoyable if you like that kind of music (look it up!). Nobody's mentioned Fallout 1 or 2 yet, which is fine by me, because the music there is closer to ambience than an actual soundtrack.
Well, I think that's about it. I think maybe I should have motivated my winner choices, I guess I'll do that later... Also, thanks for recommending Ecco the Dolphin. I looked it up on YouTube, I suspect I'll be listening to it a lot (and I usually only listen to music whilst actually playing!).
EDIT: Y'know, after some consideration I'm gonna add Freespace 2 to the list of nominees.

In no particular order I've got....
- The Secret of Monkey Island (PC on a MIDI MT-32, you can't be that!)
- Castlevania Bloodlines (Sega Megadrive)
- Severance - Blade of Darkness (PC Direct X)
- Ultimate Ghosts'n Goblins (Sony PSP)
- Diablo (PC Direct X)
Five OSTs are too few anyway :-P

1) Hitman 2
2) Shenmue (Get out of my way you old gay hoe!?!)
3) Unreal Tournament 3
4) Rome Total War
5) Assassin's Creed
Honorable Mention: Daytona USA.
"Roollllllliinnng Sstaaaaaaaaaaaaaarrt! Rrrrrrrroooolliinnng Sstaaaaaaaaaaaaaarrt!"

1. Pandora Directive
2. Under a Killing Moon
3. Grand Theft Auto
4. The Overseer
5. Fallout 3, for the first few hours until you've heard everything over and over.

You might find this useful.

make that +2, Klepacki is awesome (I actually have some of his solo stuff which I recommend for any fan of the C&C soundtracks)
Bioshock
Deus Ex
Orange Box soundtrack
Quake 2

My favs:
Halo
Advent Rising
Mass Effect
Chrome (and SpecForce)
Devil May Cry 3 SE
BioShock
WorldShift
any Star Wars game :)

When I finally met Three Dog I had to seriously stop myself from shooting him in the face. The endless repetition of those 5 tracks actually becomes mental torture after a while. If Bethesda wanted an underground music station they should have put up the cash for a decent number of music tracks. All the stuff they used was public domain anyway so it wasn't costing them anything.

It is very difficult but my favourite are
The Witcher, Silent Hill, Morrowind, Stronghold, Farenheit, Max Payne, Beyond Good and Evil, Mass Effect. Cannot say which is the best.

Five is too little :-).
So I pick some series...
Planescape: Torment
The Longest Journey/Dreamfall
Silent Hill series
Homeworld
Fallout

You are not familiar with the Sonny Bono Perpetual Copyright Act (not the actual name) are you? Those songs are not public domain.
From the Fallout Wiki:
"The following 20 licensed tracks cycle on Galaxy News Radio, listed here by song title and performer in the order found in the Fallout 3 credits. Songs licensed from APM Music, Inc do not credit performers; the composer is listed if available. "