Fruits Basket is one of those anime that I've seen once, but I'd watch again for one character (he's only in a few episodes). I know a lot of people love this anime, but I honestly don't know why. It's a little immature and I guess the majority of the audience is 14 years old or younger.
Tohru Honda is a girl who lives in a tent; her mom recently died and she was living with her grandfather, but his house is being remodeled. She told him that she would be living with a friend, but in truth she is living in a tent by herself because she doesn't want to be a burden to anyone. One day, she passes by a nearby house on her way to school. She meets the Sohmas. Yuki Sohma is the "prince" of her school. Yuki and his cousin, Shigure, walk by her tent one night and they invite her to live with them, after a landslide hits her tent, as long as she's their house keeper.
Soon, Tohru discovers the Sohma's curse. While keeping Yuki and Kyou, another cousin, from fighting, she accidentally hugs Kyou. This causes him to turn into a cat! She ends up hugging Yuki and Shigure, too. Yuki becomes a mouse and Shigure becomes a dog. The Sohmas are cursed by the animals of the zodiac. Anytime a member of the opposite sex hugs them or their body is stressed, they become the animal. Tohru promises not to tell anyone, but Shigure must tell Akito, their leader, about the discovery. Akito decides whether she gets to keep her memory or not. He decides to trust her for the time being. Akito is the main antagonist. He pretty much decides the fate of anyone and everyone in the Sohma family and also anyone who knows their secret so he causes some trouble for them.
When I first saw this anime, I thought it was ok. It is certainly not the best in any category, but it's ok. The characters seem very one-sided, mostly because each animal has their own personality and they never stray from that. Tohru is very naive and can be very annoying at times. She's constantly worrying about every little thing. Shigure and Ayame, the snake (which is my zodiac animal, too), are my favorites. Shigure can be a little lecturous and writes trashy romance novels under a pen name. He and Ayame are best friends. Ayame is Yuki's older brother and is very eccentric. Ayame and Shigure are the only reasons why I would watch it again.
Their are too many differences in the manga and the anime. The anime is 26 episodes while the manga is 23 volumes. The anime is very toned down and has alot of things that aren't even in the manga. The anime really only follows the story up until volume eight of the manga. The voices in the anime, for me, aren't the best. Neither the Japanese or the English voices are good. Both for Yuki are bad choices. Tohru's English voice is not good either. Shigure's English and Kyou's Japanese voices are pretty spot-on, though.
While it's certainly not my favorite, some people may like it. If you enjoy the younger romantic types of anime, you may like it. My advice for you, if you do decide to look into it, watch the anime first. If you don't like the anime, then you won't like the manga.