Urusei Yatsura

This cartoon spanned six films, 218 TV episodes, and ten OVAs. It was created by Rumiko Takahashi in 1981. It concerns the adventures of a group of teenagers on a slightly fantastical and often ridiculously surreal version of Earth.

The series is very light-hearted in nature and often quite bizarre.

Warning: Wikipedia contains spoilers

Only You The first movie was entitled Only You. The main characters are:

• Lum, an alien princess who can fire out bolts of lightning
• Ataru Moroboshi, a lecherous human, with whom Lum is in love
• Elle, another alien princess, who is in charge of Planet Elle
• Benten, Lum's friend

The basic plot of the first film is that the five-year-old Ataru steps on Elle's shadow during an impromptu game of shadow-tag; in Elle's culture, this is viewed as a marriage proposal. Twelve years later, Elle returns to Earth in order to marry Ataru - by which time not only had he forgotten the events of his childhood, but he was also going out with Lum. The rest of the plot focuses on Lum's attempts to prevent the marriage.