In Rakkety Tam, the villains sing a let's-get-frenzied song, which the audio book sets to a heavy beat and bass guitar.
Also in Marlfox. "Who be death? We be death! Dis de blade wot stop your breath!"
And then there's Flinky's many songs in Loamhedge. All of them are great, but the darkest is the "Vermin Lullaby", which was a normal lullaby at first, before it suddenly got Darker and Edgier in the second chorus.
"So hush now, lullaby, foxy close yer eyes, and you'll soon make lovely vittles, for the ants and flies". Squick.
The closest thing to one in the Left Behind books is Nicolae Carpathia's self-indulgent national anthem "Hail Carpathia", which gets twisted by Buck Williams into "The Villain Sucks" Song "Fail Carpathia".
A Song of Ice and Fire: "And who are you, the proud lord said, that I must bow so low..." You know Lord Tywin Lannister is badass when, in Westeros of all places, he has his own theme tune, The Rains of Castamere. It is about how, while still a young man, he wiped out Houses Reyne and Tarbeck for rebelling against the Lannisters. When it was played to another rebellious Lord they reconsidered their position. Later it is used as the signal for the Red Wedding, when enemies of the Lannisters and thousands of their troops are massacred.
"The Robber's Song" from the Norwegian children's book (and later play) When the Robbers came to Cardamum Town by Thorbjørn Egener is the three titular, not very villainous, robbers, Kasper, Jesper and Jonatan, singing about their nightly exploits. Due to the popularity of the book, the clever lyrics and the tune being a total Ear Worm, the song is known by pretty much everyone in Norway, Denmark and Sweden: