First up, They Might Be Giants "Don't Let's Start." This is my new stuck in my head default song.
I already made my sister watch this yesterday, but just because I'm addicted to this song right now, "Sax and Violins" from the Talking Heads.
This one is from the Fun Lovin' Criminals (featuring one of the deepest/best voices ever). It takes a little big to get started, but I guarantee the chorus will get stuck in your head for days. Here's "Bump".