Depends on the game, Racing and fighting games continious music.
Games that depend heavily on the storyline, the music most be connected with the events like in the beforementioned Silent Hill series is excellently done. Worth mentioning IMO is Red Faction 2 where there's no cont. background music but everytime action get's hectic there can be heard metallish music that get's my blood rushing even more, very good experience indeed.
Not so honourable mention IMO is Tekken 4, that game has some of the worst elevator music around...
