Well, I'll listen to anything once. But the bulk of my music taste stretches from the mid-1950s to the early-1990s. Say from Bill Haley, Buddy Holly, Gene Vincent and Elvis to Nirvana. Rockabilly, Rock & Roll, Surf, Folk, Psychedelic, Acid, Country (the greats, including Merle Haggard, George Jones and Buck Owens), early heavy stuff, such as Zeppelin and Alice Cooper, singer-songwriters from the 1970s (Jim Croce, Harry Chapin, etc.), punk (esp. the Ramones, the Clash and X) and some New Wave stuff. After that, it's hit or miss for me.
Among contemporary artists (even though some of these groups have been around for more than 20 years, they're still releasing albums) I like are REM, They Might Be Giants, Wilco, Primus, Rufus Wainwright, Norah Jones, Sheryl Crow, Beck, the White Stripes and Plain White T's.