I can't play much from memory, but I was so blown away that I could sort of grasp barred chords that Dream a Little Dream of me isn't horrendous. Can't sing it, but I can strum it.
If We Were Words We Would Rhyme, by Gruff Rhys
If I Had You, though I always goof the bridge
The intro to Five Foot Two, because I have heard it on so many YouTube demos and reviews.