I love this topic. It's one my friends and I (oddly, we all play guitar) have debated for years. The only answer we've come up with is that there isn't one answer. There are too many styles of guitar and music to limit it to one answer. Ultimately the debate would go something like this:
1. It has to be Jimi!
2. But Yngwie Malmsteen is the most technically gifted guitarist of all time!
3. Sure, but he has the soul of Satan. Eddie is more fun to listen to;
4. True, he's kind of a one trick pony and his real strength is song writing;
5. What about Mark Knopfler? He can fingerpick Van Halen under a table and ever note counts;
....
100. Let's get some more coffee...
So here's what I consider a fair list that takes into account several styles:
1. Most influential/varied guitarist: Jimi Hendrix (no video needed)
2. Most Technically Virtuous Guitarist that Has No Soul at All: Ynqwie Malmsteen:
http://www.youtube.com/watch?v=E6KM5XPUdvo
3. Most Technically Virtuous Guitarist with a Soul: Eric Johnson
http://www.youtube.com/watch?v=15eu7ar5EKM
I'll leave other categories open for the floor: