To-LOVE-Ru - Trouble - (Manga)

The story is about Rito Yūki, a high-school boy who cannot confess to the girl of his dreams, Haruna Sairenji. One day when coming home and sulking in the bath-tub a mysterious, nude girl, appears out of nowhere. Her name is Lala and she comes from the planet Deviluke, where she is the heir to the throne. Her father wants her to return to her home planet so she can marry one of the husband candidates, but she decides that she wants to marry Rito in order to stay on Earth. Commander Zastin has been ordered to bring Lala back and has already battled Rito. He reports to the emperor that Rito would be suited to marry Lala, after hearing Rito say that marriage is impossible unless it is with the person you love (Rito was actually defending himself but Zastin and Lala thought he was defending Lala). With this speech, Lala truly falls in love with Rito and decides that she wants to marry Rito. Her father decides that, if Rito is able to protect Lala from her fiances, then he can be her fiance, but if Rito cannot protect Lala from her other fiances, Lala's father will kill Rito and destroy Earth.

Several months later, Lala's father comes to earth to tell her that Rito was officially chosen as her future husband, but Lala refuses to marry Rito, because she has noticed that Rito loves someone else. She decides to erase the memories of her from all people on Earth with one of her inventions (Bye Bye Memory-kun), so she can start all over again on Earth. However, when waiting in front of school the next day, she finds out that her invention did not work and that everyone still knows her. Now, Lala, Rito and everyone begin a new year of high school as 2nd years.

-Wiki

Great manga and anime =)