The media player the phone comes with does support playlists, but it's pretty crap.
You can DL the doubleTwist media player which I use from the android market, it's much better than the Sony Ericsson one. It also you to play playlists imported via the doubleTwist desktop program (aka "iTunes for Android") which imports your existing WMP or iTunes playlists.
Or if it's all too confusing:
DL doubleTwist from the android market
DL
doubleTwist for your computer
Import your existing iTunes or WMP playlists
Use doubleTwist to sync your music between your computer and phone, it even converts incompatible file types
???
Profit.