Urusei Yatsura

The series begins when aliens from the planet Oniboshi invade Earth. They agree to leave only if Earth's champion can defeat the Oni champion in a game of tag within a ten-day time limit. Earth's champion, randomly selected by the aliens, is Ataru Moroboshi, a Japanese teenager with highly overactive hormones. The alien competitor turns out to be the curvaceous Lum, so Ataru relishes the idea of having to catch this beauty. However, his attitude changes when he discovers that Lum can fly. When things start looking desperate for the Earth, Ataru's girlfriend, Shinobu offers to tie the knot if he succeeds, and on the last day, when he finally catches Lum, he declares his intentions to be married. Lum misunderstands this as a proposal and eagerly agrees, since she has become smitten with Ataru. He tries to disengage himself, but Lum is adamantly faithful and demonstrates a willingness to use her natural ability to generate electric shocks to keep her "husband" in line. Later in the series continuity, Lum and some of her alien friends become more-or-less regular residents of Tomobiki and interact with the natives, who are interesting in their own right. Urusei Yatsura is unique for its premise, its immense cast of characters, and its free-for-all, anything-can-happen attitude. Too bad they can't get away with this on American TV.