There are so many possibilities, I don't know where to start
For example:
All
Half-Life games have great ambient music, sometimes more actiony.
Daikatana is worth a mention too, though it's less ambient and more traditional game music.
Doom remixes never get old, though they're mostly prominent.
Jeremy Soule is a very competent composer of non-offensive background motives, he worked on games such like
The Elder Scrolls series,
Dawn of War or
Company Of Heroes.
These are just off the top of my head.