Bright Eyes - Drunk Kid Catholic; When the Curious Girl Realizes She is Under Glass
Azure Ray - Sea of Doubts; If You Fall
No Doubt - Everything in Time (i'm not sure which version; there are two)
Orenda Fink - Blind Asylum (this song actually doesn't have any piano at all in it; it'd sound marvelous on piano, though)
Evanescence - My Immortal, Hello (yeah, cheesy, but still...)
Alanis Morrisette - Princes Familiar (the unplugged version; most of Alanis' songs have piano in them, but I can't think of any in particular at the moment).