All of it! I don't have the soundtrack yet so I don't know the names.
Knytt Underground is right up there along with Amanita Design's games (Machinarium, Samorost, Botanicula) with incredible ambient music that's an inseparable part of the atmosphere and overall playing experience. The music works really well with the visuals to create a unique world in your head that you want to get lost in.
Edit: LOVE the short piece that plays at the fairy springs (where you meet Dora and Cilia for the first time) and the similar tune in the area immediately before it (in Chapter 1)