Chulip for PS2 was pretty poorly received by the US media, but I liked it. You play as a young Japanese boy who has met the girl of his dreams. He wants to kiss her underneath a magical tree with a face, which will ensure their eternal happiness. However, he needs to win her over by writing a love letter with a magical stationery set, and the only way to get that is to kiss every man, woman, child, ghost, alien, and animal in town. They won't be so easily smooched, though, and require the solving of some sort of puzzle to get your window. It's not entirely unlike Animal Crossing in feel, but has an extra layer of weird to make it a truly strange experience.
I think this was initially a GameStop exclusive near the end of the PS2's mainstream popularity. It came with a walkthrough in the manual. Any fans?