Another decent site you could check out is
www.hxcmp3.com
They have a nice search feature that lets you search for bands that sound like (or at least say they sound like) certain bands. The search engine also lets you choose from the band's influences, names, genre, etc...
I honestly don't know how much variety they have in their selection, as I've looked for metal there almost exclusively, but I've found some mellower stuff there as well.
Some bands have lots of songs to download, some have none... you get the idea. It's just a matter of luck, I suppose.
No matter what, I'd be certain that almost everyone here could find at least one band there that they dig, and would have never have heard otherwise.