The 1980s gave birth to the mother lode of Guitar Gods so I can't say that I have a favorite. I can name the people who influenced me, though. Jake E. Lee made me pick up a guitar for the first time and learn it. Paul Gilbert, once I saw him live, pretty much blew me away so much I virtually re-educated myself from the ground up on how to even play. Even though they didn't start out in the 80s (they came from the 70s), Alex Lifeson and EVH are my chord structure bedrocks all the way. I also gained some influence from the incomparable Yngwie J. Malmsteen.
Again, there are LOTS more than this--especially when I consider everything I've heard. I'm mostly thinking of guitarists I've watched either live or whose videographed performance was so breathtaking, it actually changed the way I thought about playing guitar. There are some true greats out there but very few were doing that to me.