Thurston Moore would have to be my favorite jazzmaster player. I saw him play last week with sonic youth and it was amazing.
My favorite jag player at the moment is GUY BLAKESLEE from entrance. I also saw him play last week opening for sonic youth. He's left handed, but plays a right handed jag upsidedown, and even strings it right handed.
Jimi Hendrix is my favorite guitarist, but he doesnt count as jaguar/jazzmaster player because everyone knows he played strats almost exclusively.
John frusciante is my favorite guitarist that is still living, and from what I understand he uses a jag quite a bit with solo stuff; I still think of him as a strat player though. It was him and Hendrix that inspired me to get a strat.