In the Stage 7 cutscene, Lammy goes through a number of flashbacks as she rushes to the MilkCan concert. One of them involves Katy trying on different costumes and asking for Lammy and Ma-San's opinions on each one. Lammy is too busy working with electrical equipment, and Ma-San is reading a book and doesn't care about what Katy wears. Lammy then plugs in the electrical cord, electrocutes herself, and the electrical surge results in her hairstyle turning into an afro, which Katy and Ma-San really like.
Katy: Lammy, that's it!
In PaRappa's side-story, P.J. Berri's definition of "rock n' roll."
Another from PaRappa's side story. He, PJ, and Sunny are helping with Milkcan's performance in various ways. Sunny's helping to design costumes and shows one to PaRappa. He then requests to 'see it from the side...'
A third one from PaRappa's side-story, in Fright Flight, you get this nice little subversion of the typical call and response format of the game:
Fussenpepper: I'll miss my train. PaRappa: You'll miss your train. Fussenpepper: I miss my brain. PaRappa: May I help you?
At the very end of the intro cutscene in "Noodles Are the Flow, Noodles Are the Groove," there's yet another "I know! I gotta believe!" scene. The kicker? Instead of PaRappa saying it, it's Colonel Noodles.