Winamp is out there for the Droids if you like that sorta thing. If you know what mp3's are, you are probably aware of Winamp on PC's.
I personally dont like having to buy a huge SD card to lug my music around on, so I prefer streaming options like Grooveshark, Yahoo music, Slacker radio, and of course XM/Sirius apps if you subscribe to those services. Pandora and LastFM also have very nice streaming apps and are free. Rdio is another highly praised social music streaming app, but Ive never used it.