Urusei Yatsura (Vol. 1) (Episodes 1-4)

When the Oni, a mysterious race of Aliens [Urusei Yatsura - 'Those Obnoxious Aliens'], come to repossess the Earth, they give us one chance to save our planet - a champion, selected at random, must defeat their Princess Lum, in their national sport - Tag! Unfortunately for Earth, the champion turns out to be Ataru Moroboshi, a lecherous lad whose lack of luck is legendary. When Ataru lays eyes on the lovely, curvaceous Lum, he readily agrees to take on the task of touching the tips of her tiny horns, but alas, when the contest begins, he find out that the Oni forgot to mention one small matter - Lum can fly! When all seems lost, his girlfriend Shinobu promises to marry him if he wins. Win he does, but Lum misinterprets his victory cry as a proposal of marriage - to her! Now Lum's living in his closet, planning their wedding, and zapping him with high-voltage electricity if he even looks at another woman. His girlfriend isn't sure if she's been jilted or saved from a life of misery, his Lum-crazed schoolmates are plotting to get him 'out of the way', his parents are loudly wishing he's never been born, and to top it all off, a demented Buddhist Monk has been seen lurking around the neighbourhood mumbling something about evil spirits and curses. Then Lum's friends and relatives start visiting, and things start to get really weird!