Tama-chan is a flying, myuing hot springs turtle, one of the main characters in Love Hina.
The abilities of Tama-chan (as well as most of the other hot springs turtles seen in the series) are far beyond those of a normal turtle. First of all, Tama is capable of soaring through the air like an albatross, on sea turtle-like flippers. Second, Tama has the ability not only to speak (her speech sounds like the mewing of a kitten!), but also, as seen in the manga, to write.
For some reason, Motoko is terrified of Tama-chan. Kaolla occasionally attempts to make Tama into turtle soup, attempts which are foiled either by Tama's ability to fly or by one of the other human characters stopping her. Tama-chan is not to be confused with the strange mechanical turtles breeding below Hinata Inn, which are just... evil.
I suppose Tama-chan officially classifies as Love Hina's obligatory cute anime animal. Kawaii!
(No, I'm not misspelling 'myuing' - Tama's sound effect, as seen in the manga, is 'Myu'. This is also what she writes on a note to the humans.)