I'm a little late to Regina Spektor (Begin to Hope came out in June 2006), but damn she's good.
Each song gets a little better everytime I listen to it. Someone said she was the next Sarah Maclaughin but I think she's better than that. I was/am? a SM fan, so no judgment here, but her lyrics are smarter and laced with something a little stronger than heartache and bad coffee (all good things, no doubt).
I think she plays the piano in most of her songs, because 1) she was classicly trained in piano according to amazon, 2) there's a lot of piano in each song, and 3) no one else is credited in jacket. I wouldn't say any of her songs are happy, per se, as a matter of fact most of the lyrics are pretty sad, but the music is so happy, lively, and dare I say quirky? that there's nothing depressing about the songs themselves.
I could go into intimate detail with each song, but I'll leave that thrill to the listener. Check her out. You can listen to one of the songs here: http://www.spinner.com/2007/07/15/women-who-rock-right-now-no-5/