Preferably some kind of supernatural / sci-fi / fantasy or the like.
It's fine if it's only available in Japanese.
Example:
Murasakiiro no Qualia
Spoiler (mouse over to view)
Gaku and Alice fall deeply in love in many of the parallel universes. However, while it is a very important occurence for the story to move forward, the story is in no way supposed to be a romance.