No worries.

Updated. Thx Nitrotab.

http://store.steampowered.com/app/4560/
Company of Heroes' soundtracks on steam. Not sure if they're permanent additions or not

Thx. Also on Steam, "Greed" soundtracks.

Updates :
Invincible tiger (complete, cool musics)
Baldur's gate (weird remixes, you have to be a fanboy to enjoy them)
Flock ! (complete)
Panzer general (complete)
Edit :
Good old Soundtracks from Mark Knight's website :
- Alfred Chicken
- Captive 2 : liberation
- Cyberspeed
- Duke Nukem : total meltdown
- Dungeon Keeper 2
- Populous
- Supersonic racers
- Warhammer : dark omen

Back on Tim Wright (aka CoLD SToRAGE)'s website, some details concerning game soundtracks contained in his big Amiga MODs pack (direct link to the zip file):
- Agony (2 MODs)
- Aquaventura (5 MODs)
- AWESOME (8 MODs)
- Carthage (5 MODs)
- Leander (9 MODs)
- Magician's Castle (appears to be an unreleased game) (11 MODs)
- Microcosm (12 MODs)
- Phoenix Rising (apparently a Genesis/Megadrive game that used MODs) (7 MODs)
- Powermonger (1 MOD, intro)
- Puggsy (Demo) (4 MODs)
- Sensible Soccer (don't know wich one) (6 MODs)
- Shadow of the Beast II (14 MODs)
- Shadow of the Beast III (19 MODs)
- Tentacle (appears to be an unreleased game) (5 MODs)
The other MODs seem to be from good old Amiga demos.

Thx. Also, some Earthrise songs.

Ooooh... a NICE useful thread.
One of my darkest secrets: old Doom music http://www.sirgalahad.org/paul/doom/
edit: oops, only now I see, you want official sites only, and this is far from official. Still, it's not quite the original sound files, they were remastered or otherwise modified somewhat.

Is this only for games?
If not, I'll hand you the soundtrack to the open-source movie: Elephants Dream.

Bah, let's do it ! The movie looks like a video game anyway. :D
Edit : if there are enough free soundtracks for movies, maybe we'll make another thread.

I guess it will pretty hard to find, or at least for soundtrack from movies produced by big companies I'm afraid.
There are tons and tons of games (even "big games") which never see their soundtrack released officialy, movies or just the contrary.
Still a good idea though, if we can find interesting free stuff.

Yes I agree that the list won't be as big for movie soundtracks. Btw, Elephants dream is a very nice soundtrack.
Edit : speaking of elephant, I added the Zoo empire soundtrack.

The soundtrack to Arcanum: of Steamworks and Magick Obscura can be downloaded from fansite Terra Arcanum (don't be fooled by the .exe extension on that link, you'll get to a page where you get a link to download the soundtrack). Though that site itself may not be not official, there is a link to it from the composer's site.

Heh, yes, Terra Aracanum as a whole seems pretty broken. And that is also just their mirror of the old Sierra Arcanum website (such mirrors are almost always broken in some ways), not the actual Sierra website (that one got taken down long ago and now redirects to Activision).