Looking for an Anime like Fruits Basket

I would say Ouran Highschool Host club, Kamisama 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 love 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 space where she doesn't necessarily have a place, but then she kind of helps out and is able to gain everyone's love and friendship..It's a really cute anime with very funny parts, and touching ones as well
Hope this helps! Let me know what you think of them! (If you watch any of them XD)