The BGM during the Pyoro minigames becomes faster and gains more instruments as your score increases, eventually becoming surprisingly rocking.
Wario Ware: Mega Party Game$ has Shinobi Game aka "Stealth Turtles", which plays during Kat & Ana's turtle-balancing game.
Wario Ware: Twisted! has the Mona Pizza jingle, in both English and Japanese. Dribble and Spitz's stage lets you choose the accompanying music; amongst the choices available are the Taxi Symphony and Dribble and Spitz's instrumental theme.
D.I.Y. has some pretty good tunes too, like the song that accompanies Jimmy T.'s stage, and many of the preset records. Mona's are remixes of classical music, Jimmy's are inspired by all kinds of musics throughout the world, Ashley's are easy to sing to and make up lyrics for, Orbulon's are weird, space-themed tunes, and 9-Volt's are good old Nintendo tunes remixed. As for whether or not the tunes players create qualify, that really depends on their skill.