Karthus's ult and Nessun Dorma.
He should sing the very last notes from Nessun Dorma or any great opera classics.
Does he do that in the Italian version of him? Is there an Italian dubbing of League of Legend's champion?
It fits so well because "vincero" means "I will win" translated to English.
VIIIINCERROO!!!!! PENTA-KILL!
This should also be global and if you are near Karthus then it sounds like a an undead choir is harmonising with him as he belts, "VINCERO!"

EDIT:
Mordekaiser has his ultimate to show how he plays around with the soul of his victim in gameplay. Hecarim has ethereal horsemen to show his theme. Thresh has his passive to show how he likes to play around with souls. Karthus needs something more than he has now and it would be great if souls around him sang haunting melodies whilst he's killing people.