In the Bleach fandom, Humble Shopkeeper has one of the characters declaring she wants a villain song to "underline [her] bad-ass-ery". It involves the line "I'll paint the moon red with his blood", a chorus of wolves and evil laughter. Since it takes place in a realistic setting, it's pretty much as weird as it sounds.
Cyros from The Legend Of Spyro: A New Dawn gets "Into The Great Unknown", which she uses to scare her brother Pyrus into aiding her Evil Plan. Later on, she gets "Let Your Secrets Out", where she uses her powers to cause Cynder and Ember's hidden feelings to come to the surface. She also gets a short spell later on that transfers Empress Tyrania's energy into a jewel she can use. Justified in that she is an egotistical music lover and a Evil Diva who uses songs to cast spells.
Cyros gets one more during the Finale called "Welcome To Your Final Show", which is pretty much a straight up Villain Song about how she intends to kill her brother and Ember, all the while using her Musical Assassin powers to try and do so. She was Drunk on the Dark Side at the time, so naturally she's more hammy than usual.
Decks Fall Everyone Dies plays this straight and sort of subverts it. Duke gets a villain song in which he gloats about how he reigns over everyone using dice games and sexiness, but in the very same song, he hints at a nagging sense of guilt over it.
In the Pony POV Series, Princess Gaia, Fluttershy's Super-Powered Evil Side and the second Big Bad gets two. The first is a ponyified version of "Come Little Children" from Hocus Pocus and the second is a Dark Reprise of Fluttershy's "So Many Wonders" song, telling how her world is safe and perfect and no one will ever have to leave it... And will forget their old lives entirely. It also serves a purpose, as she's an Evil Diva who can trap ponies through song.
Discord has gotten several. His father, Havoc got one called "Here's To Chaos" as well.