Cheap Cheap: Here, I've got a little sample. PaRappa: Here, I don't have a sample.
Um Jammer Lammy
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.
In general, given the relative freedom that a player is provided with when rapping (especially during Cool mode and 2-player versus games), it's very much possible to use the word clips available at disposal in such a way that Hilarity Ensues.
Depending on the available words, a player can easily rearrange them to form something new, such as turning "What's your/my name, fool?" into "What's your/my full name?", creating "I've got a TV" or "Put my show back on TV" from "Put me back son, you know I gotta go/I'm gonna miss my favorite TV show", and making Colonel Noodle say "N-O N-O N-O N-O" during the "N-Double O-D-L-E-S" part (all three being examples from Parappa The Rapper 2 done in "Chinese"). It's also possible to form less appropriate words/sentences this way.
Within context, each and every word available to the player is completely clean. However, due to the pronunciation of a few words in some cases (namely "for" and "five" in Parappa The Rapper 2), a player can easily change the way they listen to these words, leading to them appearing to sound vulgar. The most notable example is the "Thanks brother" part in Parappa the Rapper 2 where mashing the L button makes Parappa/Colonel say "For you/me", which can also sound like they're saying "fuck" instead of "for".
Alternatively, the player can also press or mash random buttons to produce lyrics that make little sense, lyrics that make NO sense, stuttering, and spaz attacks. To add even more fun to the mix, there are also default commands for buttons that don't have any action mapped to them (a.k.a. Parappa saying "Oops!" or "Uh-oh!" when an unused button is pressed) and instead make the player character suffer some sort of hindrance (such as slipping and nearly falling, having a bug jump out of the carpet and a stove next to them combusting), and the best part is that NPCs have this as well when playing a 2-player versus game.