The entire bathroom rap, especially when you enter Cool mode.
Or when you fail, in which the Potty Failure is depicted as a rocket taking off inside PaRappa, as a way of indicating that he pooped his pants.
In the Stage 7 cutscene in Um Jammer Lammy, 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 in Um Jammer Lammy, P.J. Berri's definition of "rock n' roll".
Another from Pa Rappa's side story in UJL. He, PJ, and Sunny are helping with Milkcan's performance in various ways. Sunny's helping to design costumes and shows one to Pa Rappa. He then requests to 'see it from the side...'