Definitely an alto sax. Not kidding. If you had to equate genres with instruments the sax and jazz would be perfect. The sax and piano (rag-timem etc.) pretty much created jazz.
Pretty much brass/bass instruments go well with jazz, though. Woodwinds are kind of iffy, especially the flute. (I do understand the sax is a woodwind but come on, everyone knows it's a brass posing as a woodwind). Clarinets can get away with jazz, too. Strings are kind of iffy, too, as in classical strings. I've never heard of a jazz violin, but you never know. Contra bass would definitely be jazz on the other hand.
So. Alto-sax, trumpet, trombone, bass guitar, and clarinet in order of best to least best. (Excluding piano cause piano is the BOSS)
I think that it all depends on how well you know the instrument in question. Jazz can sound HORRIBLE on guitar if someone doesn't know what they're doing, just like free form jazz played on piano could sound like total crap.
But personally, I like bass guitar. It sounds so funky and awesome!