EDIT: Belated but honorable mention to Mega Man 2. Yes Jarret, that game did have an awesome soundtrack...
I was a very late bloomer when it came to music. I think before high school, I could only say I knew the works of two artists: Michael Jackson, and Weird Al Yankovic, whom I discovered through his parodies of the late pop singer.
Having said this, there was video game music I was absolutely passionate about as a kid. To this day, one of my favorite video game soundtracks of all time belongs to Final Fantasy IV (which was Final Fantasy II in the States, at the time I played it), scored by the legendary Nobuo Uematsu, who managed to move my heart with just about every 16 bit digital midi track* he put into that game. From the adrenaline pumping battle music, to the whimsical character songs and victory fanfare, and finally the sorrowful songs that would play whenever tragedy struck your party.
I used to pause the game (assuming the music kept playing) and lay down on my bed just listening to what was probably a 2:00 minute loop of the song over and over again. I did this with a few games - only my super duper personal favorites (one in particular I've mentioned before) that I would have scoured the internet and downloaded at the time, had that been an option. Super Castlevania IV, a few tracks from Street Fighter 2 (random, I know), a lot of stuff from A Link To The Past, and even the final stage in Little Nemo: The Dream Master.
I don't know if it left me with an 'unrefined' taste in music - but heck, even if it did, I don't think most people got to really experience music like I did as a kid. To have this intense, operatic score start to blare right as the party you spent 50+ hours with, traveling and fighting along on a journey prepares to fight this awe encompassing final battle against Zeromus - a demon from another planet (the second moon, to be precise) - is nothing short of mind-blowing.
Video game music shifted once it became pretty much like real music. And with a few exceptions, sadly it's just not as memorable anymore - though this could just be me finally having some legitimately great music compare it to*. There was just something about being that age at that time, having that level of interest in games/lack of interest in 'real' music that made for the perfect storm of...well, me being a huge geek about this stuff.
Currently Playing: Just beat Prince of Persia, and of course they got me to download the epilogue right away (I still don't know how I feel about giving us the cliffhanger ending just to ensure we download the rest of the story), and after owning the Orange Box for nearly two years I can finally see the light at the end of the tunnel with Half Life 2 - of course with Parts 1 and 2 still waiting to be touched. After reading a glowing review from Mr. Justin McElroy, I decided to try out the point and click adventure game Ben There, Dan That, and quickly followed that up with a purchase of Time Gentlemen, Please! Dabbled a bit in an enjoyable, discounted N+, and I finally got around to buying (but not quite yet unwrapping) Professor Layton and The Curious Village.
*I may be butchering the terminology - again, late bloomer
*Nothing's the matter, Mr. Joel, I'm sorry I got you started on that tangent
*Obvioulsy I'm referring to Fall Out Boy