My personal favorite is Giants 3B coach Tim Flannery, whose music has taken on a vaguely "Americana" tone lately, though his Irish heritage is a big influence. Another journalistic reference for me- I've interviewed him twice, once for a music article and once for a baseball one. He's a fine singer and musician (and Jackson Browne's his old surfing buddy, apparently).
Who else is there?
Barry Zito - guitarist, musical family- sister Sally Zito's a good piano-based singer-songwriter
Bronson Arroyo - grunge guitarist/singer
Jake Peavy's a guitarist too, I believe. Don't know what his music's like. Seems like it's mostly pitchers.
There's also tons of ex-players- Scott Radinsky's a punk rocker, Bernie Williams has guitar albums out, Jack McDowell had a decent alternative band for a while. Who else? Is a complete list possible?