A God Am I: Nappa jokingly implies this a couple of times.
In Castle Crashers when he's riding on the crocodile he wails on a small horde of enemies with ease:
Nappa: Look at this shit! I'm a fucking God!!!
Then in Magicka, when Vegeta gets killed again and Nappa has to revive him for the hundredth time.
Nappa: Luckily I'm around to be your.....hehe.... I feel like I'm your Jesus at this point. I was gonna point out the irony of me constantly saving you, bringing you back to life. Vegeta: Shut up Nappa......
Berserk Button: Vegeta really doesn't like being reminded that he's a member of Krillin's "Team 3 Star".
Oddly, Vegeta gets mad at the thieves for looting bodies in Castle Crashers.
Oh, and never refer to him as Kakarot's minion.
BFG: In their Magicka playthrough, Nappa has a gun, which Vegeta ends up getting. Most of the playthrough is them just shooting everything.
Parental Neglect: Trunks gets mentioned a few times. Vegeta completely ignores him.
Vegeta: Apparently I have some like kid or something now. It's weird. Nappa: Did you name him Vegeta like your father always wanted? Vegeta I don't know what the damn thing's name is!
Rock Falls Everyone Dies: The beginning of Borderlands 2, which features the four main characters getting blown up in a train. While they're supposed to survive, they're treated as dead by Nappa and Vegeta (who play DLC characters Gaige and Krieg respectively).
Throughout the entire Killing Floor playthrough, Vegeta determination to have fun slowly wanes into desperation until the very end, where he's screaming angrily that they're having fun, while Nappa is sobbing and begging for it to end.
Krillin, by way of Vegeta locking him and forcing him to play Slender The Arrival, has shown this in spades throughout the playthrough. It's very noticeable during the second episode, when he survives a 17 minutes of a full-aggro Slender Man after he has trouble finding the last page.
Sir Swears-a-Lot: Vegeta, and how. Nappa's got a bit of a foul mouth too, but not as bad as Vegeta.
Vitriolic Best Buds: Nappa's convinced that he and Vegeta are this, though Vegeta doesn't do anything to show that he considers Nappa a pal. However, Vegeta does seem to show less contempt towards Nappa than he does in Dragon Ball Z Abridged's first season.