I’m usually not a big fan of finger picking unless I’m doing banjo rolls but really, that doesn’t count. There are a few that I enjoy finger picking though.
Goodbye Young Tutor, You’ve Now Outgrown Me by Say Anything is a fun one to play but it’s an awfully sad song.
Crush by Cory Branan is a pretty good one.
I also like Billion Bees by Kevin Devine. It’s a pretty sweet one.
I finger pick all the softer parts in Buckethead’s Soothsayer. It’s not meant to be finger picked but it’s fun to do. The whole song is easy until Buckethead takes it over the edge. I can’t keep up with that though.
Like @Schroedes13 mentioned, you can pretty much finger pick any song that you know the chords to. Just hold the chord and play around with the strings. It’ll sound like the song but it will give it a different twist. Just have fun with it.