Mostly, I like variety. Here are some of my favorite styles are(with a few examples):
Rock--Beatles, Springsteen, The Who, Toy Matinee, James Gang, Blue Oyster Cult, Led Zeppelin.
Pop(not the current bass heavy, over-Melodyne processed vocals, teen stuff that is so popular these days)--Beatles, Marshall Crenshaw, Squeeze, Warren Zevon, Kirsty MacColl.
Blues--B.B. King, Albert King, Tommy Castro, Chris Cain, Walter Trout, Robin Trower, Robben Ford, Gary Moore.
Jazz--Steely Dan, David Sanborn, Joe Sample, John Coltrane, Miles Davis, Dave Brubeck.
Prog--King Crimson, Yes, Ambrosia, Pink Floyd, Be Bop Deluxe, Gentle Giant, PFM.
Acoustic--James Taylor, Dan Fogelberg, CSN&Y, Simon & Garfunkle.
Classical Guitar--Muriel Anderson, Laurence Juber, Preston Reed,
Electronic music--Synergy, Tonto's Expanding Head Band, Tomita, Jean Michel Jarre, Massive Attack.
Early R & B--Drifters, Sam & Dave, Supremes, Chakka Khan.
Southern--Allman Brothers, Poco, Pure Prairie League.
Classical--Grieg, Tchaikovsky.
I also like a little bit of country music--mainly older stuff. I find I get tired of the newer stuff because it starts sounding the same after a while.
Regardless of style, I generally like earlier releases from many artists--usually the first three or four albums. It's unusual for an artist to keep my interest after that, they start repeating themselves or they change so much that they're unrecognizable from the early efforts. Peter Gabriel and Joe Jackson are ones who managed to avoid that situation.