Belasco is the ruler of a demonic dimension called Limboes.
He's a demon king, an ancient magician who owns a powerful artifact : the soulsword. He had a loyal servant : an evil doppleganger of Kurt.

Kurt has fought Belasco on numerous occasions. The most famous one is their first encounter (Uncanny#160).
Belasco trapped the X-Men in Limboes and stole seven years from Illyana Rasputin (Colossus's sister) : all of her innocence...
He wanted her to become his apprentice, but she finally overthrew him.

Years later, Belasco returned several times but Nightcrawler, the X-Men and Amanda Sefton have always defeated him.
If he's truly dead remains to be seen... ( Excalibur#103, X-Men unlimited#19, X-Men : black sun)

Amanda Sefton/Magik II is now the new ruler of Limboes. (as seen in the "X-Men : Magik" mini, then in the "Nightcrawler" ongoing) If Kurt has a "nemesis", it's probably Belasco.
 

Ironically, in the Universe X maxi-series, by J.Krueger and Alex Ross, and which takes place in a far future, Belasco has always been... Nightcrawler, displaced in time, amnesiac, and fighting the X-Men from the very beginning. When a resurrected Captain Marvel tells him the truth about his origins, Kurt/Belasco comes back to the side of the angels.