Pandora
This was the first place where I started listening to music online. I like that with Pandora you can create different stations based on artists or genres that you like, then they'll automatically generate a playlist based on your preferences. This was a great way that I found a lot of new artists while I was rockin' out at work (AND working of course:-)).
Imeem
Initially I went to Imeem to search for specific artists or songs, then create playlists, but the user interface is extremely aggravating, so I don't go there often unless I really want to hear a specific song, and I'm too cheap to buy it on iTunes.
Lala
Lala on the other hand has become one of my favorite places to listen to music. The user interface is clean and easy to use, and I love that along with listening to thousands of artists on their site, you can also upload your own music library and discover new music through following other users and their music tastes. They also have the option of creating 1 hour mixes of a specific genre.
All in all I'd say Lala is the best, but check them out for yourself.
Happy jammin'!