I agree that music has a great effect upon the games that I play.
Among every game I can think of, there's always at least one song that has stuck in my head that I can always remember and refer to the game through, ranging from Kirby Superstar with King Dedede's theme to Modern Warfare 2's Boneyard Flyby theme. The only game I can think of that I do not actually recall a song for is Bioshock as that game's atmosphere allows the lack of music to work perfectly. The songs really do highlight parts of the game and make the experience so much better. They make Resident Evil 2 even more creepier, Call of Duty so much more action packed, etc.
One of the reasons I got into Touhou was of course, the music. I heard one of the songs and that got me hooked into the series. The songs always feel perfect for the area that I'm in and get me more into the game than without it, though it does distract me of my focus at times. My first attempt against Flandre ended incredibly quick because I was too busy singing too her theme to actually notice half the bullets. Either way I would of died as quickly as I did. Fun to make excuses though.