Looking for an 日本动漫 like Fruits Basket

I would say Ouran Highschool Host club, Kamisama 吻乐队（Kiss） and Starry Sky would be similar.

'Kobato' is a great anime, very sweet and heartwarming
I also suggest 'Special A' which is very similar to 'Kaichou wa maid-sama'... both are really great 爱情 stories which face trials and challenges
Above all else I recommend 'Akagami no Shirayuki hime' (Snow white with the red hair is the English name) It's similar to fruits basket because there is one girl who kind of meddles her way into a 太空 where she doesn't necessarily have a place, but then she kind of helps out and is able to gain everyone's 爱情 and friendship..It's a really cute 日本动漫 with very funny parts, and touching ones as well
Hope this helps! Let me know what 你 think of them! (If 你 watch any of them XD)