I'm very picky when it comes to music. I suppose the first band I ever got into was Journey. My mom used to listen to Journey as we would drive across the country back and forth between Utah and North Carolina, and that was basically the only music I knew. I never took any notice of any other music at that time. Except maybe the Spice Girls, which she also listened to, but other than that I didn't know anything else existed.
My real musical education started with Nirvana in sixth grade--they were ground zero. I suppose I listened to other bands for a few months before then--Blink 182, Alien Ant Farm, Ozzy Osbourne, Black Sabbath...basically just some music someone had given me, because at the time I didn't know anything about music. I quickly forgot about some of the s**tter ones fortunately though (Blink 182).
Then the Doors came along with Radiohead, Depeche Mode, the Foo Fighters, the Beatles, and finally, an obsession which lasted me a VERY long time, the Queens of the Stone Age. That's a love that will pretty much never die. Nirvana was the bridge to Queens of the Stone Age, and Queens were a bridge to a whole host of other tastes in music. I started listening to Kyuss a lot too. I enjoyed listening to the Wipers for quite while, I discovered PJ Harvey, and then I found the Pixies a few years after that. Let's just say I fell instantly under their spell.
Then, one day I discovered Labradford by chance on Last.fm. I love listening to Labradford, their music is really good to fall asleep to; it gives you the best dreams and just makes it really easy to fall asleep. Labradford then led me to my current musical loves, Slint and Polvo. And now I'm exploring similar artists.
There's a lot more history than this, I just really can't remember everything right now. I really love the music from Squaresoft's Final Fantasy IV, VI, VII, VIII, IX, and Chrono Trigger--those have all been big influences on me.