Randy Rhoads!
1) Style
There were guitarists before Randy who mixed up classical and rock influences (Blackmore, Schenker), and guitarists since who've done the same and taken it to the extreme (Yngwie), but Randy remains my favourite guitarist to have blended both worlds. "Diary of a Madman" and "Revelation (Mother Earth)" are particularly excellent examples of his approach to classical arrangements in rock song structures. His best solos are emotional, melodic and totally ripping.
2) Songwriting
I love Iommi's riffs in Black Sabbath, but none of Ozzy's post-Sabbath songwriting partners have done the business with the regularity and consistency that Randy Rhoads did. Everything he did with Ozzy remains a totally essential rock track - no filler.
3) Died in his prime
Of course, the "no filler" aspect is understandable considering that Randy died after only a couple of years in the spotlight; he never had time to grow old and stale, or to have a Damascene conversion to the blues like Gary Moore and Vivian Campbell, resulting in endless boring albums of neo-classically-influenced Robert Johnson covers.
4) Cool guitars
I'm not going to put "tone" on this list because I don't think Randy really had an exceptional guitar tone. It's a bit too raw and trebly for my ears. But the array of awesome guitars he played gives me cold sweats and fevered dreams when I think about them too much. The white Les Paul Custom, the polka-dot Sandoval V, the black Jackson Rhoads prototype, the white Jackson "Concorde" shortfin V... tasty.
5) Inspiration
Randy was the first guitarist I really desperately wanted to play like. I had already been exposed to Hendrix, EVH, Michael Schenker, Satch and Joe Perry as influences when I got into Ozzy, but although I loved their guitar playing it wasn't until I heard "Crazy Train" that I became acquainted with the joy of sitting listening back to the same riff twenty times to catch every nuance, or dissecting the solo licks until I was 100% certain that I was nailing them just like the record. I already knew the guitar was cool, and I loved playing it, but it took Randall William Rhoads to get me truly stoked about the possibilities of playing the electric guitar.