I want to add a couple of other guys who deserve honorable mention, if not more. They are extremely versatile, but probably not most versatile - I think those have been pointed to altready.

Bruce Cockburn - need I say more?
Duane Allman - no one, I believe mentioned slide guitar (which is why I, personally, think Ry Cooder is the man). And DA played a real nice acoustic, too.
Marty Stuart - He's a little bit country and a little bit rock 'n roll, a real sharp dresser and he's a whole lot more. He's also a monster on the mandolin. Check out a recording called "Busy Bee Cafe" (I think that's the name) for some really fine picking by him and others.

One name I'm gonna put out is a man known for his mandolin playing, but who was a very accomplished all-around musician - the late Jethro Burns. I had the distinct pleasure of working with him a few times and never met a nicer gentleman, or a more inventive, clever, brilliant musician. He has a number of recordings on Flying Fish that show his jazz chops. Or you could hear him on many of Steve Goodman's recordings.
BTW, Jethro's son, John Burns, is an incredible guitarist, singer, writer and all-round good guy. He can be heard on some of John Prine's stuff; he backed up JP for years as part of the Famous Potatoes. And I think he's working on his own stuff in Nashville. I guess growing up with Jethro as father and Chet Atkins as uncle must have rubbed off.