I may come off only liking speed (Although it does hold a special place in my heart)..I do like slower pieces from the 50's on. My grandparents turned me onto Les Paul and Mary Ford, and swing and jazz of that era when I was younger. I love many bands from that generation as well.
I also like Southern rock and modern country as well.
I started learning guitar because of Randy Rhoads..but Yngwie J. Malmsteen is my biggest influence.