I became engaged in a conversation with one of my students today, about how certain musicians develop their own sound. Carlos Santana said that your grandmother should know it is you from one note .... I started running down my list of notable players who have achieved this...  
 
Jerry Garcia, Carolos Santana, Mark Knophler, Stevie Ray Vaughn, Michael Houser, Trey Anastasio, Jimi Hendrix, David Gilmour/Roger Waters... More to follow. Please add. Edumacation is mighty important.

Frank Zappa.

Here are a few on the bass side... John Patitucci, Percy Jones, Marcus Miller, and Jaco of course. On the guitar side I'd have to add Frank Zappa.

Glad to see that I'm not the only Zappa fan

Chris Squire, John Entwistle, Paul McCartney, Al DiMeola, Adrian Belew, Robert Fripp, Keith Richards,  Allan Holdsworth...

Billy Gibbons

i definitely don't agree with trey anastasio. he sounds like the culmination of every other hippie jam guitar player there has been.
people that have their own sound?
fred frith, nels cline, derek bailey, elliot sharp, mary halvorson,  blood ulmer, duane allman, d boone! , kurt rosenwinkel, jonathan kreisberg, JIM HALL, adam rogers, wayne krantz, oz noy, so many more.
 
(Message edited by darkstar01 on March 13, 2008)

I have to disagree with your disagreement on Trey Anastasio - I haven't been into Phish for almost 15 years, but his playing is still very melodic and special to me when I listen to old shows. To me, his compositions transcend the mere adjective hippie.
 
I don't have any one to add to the list, so I guess I will just second Jimi Hendrix.

Warren Haynes. No matter who he is playing with (Gov't Mule, The Allman Bros. Band, Phil & Friends, etc) you instantly know who is playing guitar. Rock, blues, jazz, he still sounds like Warren.
 
Have fun, Mike, tho

I can tell Steve Howe's playing anywhere (and I'm a bassist!).  
On bass, percy Jones has a pretty distinctive tone as has billy sheehan.
 
Graeme

Phish gave hippies a bad name. I really am not too into his music anymore, but his guitar sound is pretty distinctive. I saw lots of mediocre Phish shows, but I saw maybe 12 that were pretty great. Colin

Bruce Hornsby; Gary Burton; Itzak Perlman

The minute you hear the first note from that Spyder, you know WHO it is. Same goes for Clarke, McVie, and Mark King. All of these gentelman played Alembic basses but they all had there own sound.

Stanley Clarke,Paul Jackson (Herbie Hancock) Victor Wooten
BB King, Wah Wah Watson
Lee Oskar (harmonica)

Dont forget about good old Rick Danko. Even though he was not a Alembic player, he had an unmistakeable sound. The same goes for Robbie Robertson.