After watching the Fruits Basket anime, I was interested in reading the Fruits Basket manga to see how the anime compared to the original source material. I have read through volume 20 of the manga, and these are the observations that I made. The Fruits Basket anime only covered the first eight volumes of the manga, so reading the later volumes of the manga was rather eye-opening.
The anime basically follows the first volume of the manga with very little changed. The only real difference is the fact that the character of Shigure is a little more lecherous in the manga compared to his portrayal in the anime.
In the anime, when Hana and Arisa visit Shigure's house, there's a card game they play, and the three Sohma family members accidentally keep changing into their animal forms. However, in the manga, the Sohma family members never change into their animal forms, and the card game is extended out. Also, during this section of the anime, we get a one-sentence background on Hana, and a brief flashback of Arisa's past and how she met Tohru. In volume seven of the manga, we see a more detailed view of Arisa's past and how she and Tohru met. In an even later volume of the manga, we learn a lot about Hana's past and her "wave power."
In the manga, there is a reference to a hat that Tohru got when she was little. Tohru had run away and become lost, and a strange boy came to her and helped her. Before he left, the boy put the hat on her head. The hat is never mentioned in the anime, but references to the hat appear numerous times throughout the manga.
Another difference between the anime and the manga is the fact that Momiji actually runs into Tohru before the Cultural Festival in the manga; she's at work at the time. Also in the manga, Momiji also tells Tohru about his father owning the bulding that Tohru works at before the Cultural Festival. Haru is also introduced earlier in the manga (in the manga, he first appears at the New Year's Celebration, and is seen talking with Shigure). Tohru also finds out about Hatori's Zodiac self differently in the manga. Instead of finding out before New Year's, she finds out in January. Hatori is out in the city and sees Tohru; Tohru slips and Hatori catches her.
In the manga, it is also revealed that Tohru, Yuki, and Kyo's teacher is named Mayu, and that she is a former girlfriend of Shigure. When the reader reaches volume nine of the manga, characters start appearing who are not in the anime: Rin Sohma (the horse of the Chinese Zodiac, and a love interest for Haru), Kureno Sohma (the rooster of the Chinese Zodiac, and a potential love interest for Arisa), Kakeru (the vice-president of the school student council under Yuki), Machi (a student council member), Kimi (another member of the student council), and Nao (another member of the student council). There is also more background information given on Yuki and Kyo's parents, and the relationships between the parents and their sons. We also learn more about Momiji and his little sister, Momo.
One part that appeared in the manga that I wish could have appeared in the anime is the "Sorta Cinderella" play that is put on by Tohru and her classmates. It's a very hilarious section in the manga, and it would have worked so well for the television format.
Once you get past volume eight of the manga, so much more information is revealed about the characters and the Sohma family's curse. If you're a fan of the anime and wish the story would continue, I would recommend reading the Fruits Basket manga series. While the anime did a pretty good job of bringing these characters to life, I felt I knew the characters even better and liked them even more as I read the later volumes of the Fruits Basket manga.