Devil Fruits can only be eaten once. It's rumored that if you eat more than one, you'll die.
There are also one of each kind of Devil Fruit, and only when a user is killed will another one of the same kind be found.
Devil Fruits are also very rare in East Blue, as well as the North, South, and West Blues, but are very common in the Grand Line and the New World. You'll be seeing a lot more Devil Fruit users after this Saga.
There are three categories of Devil Fruits:
Paramecia - Commonly called the weakest of the types. Paramecia Fruits, when eaten, affect your body, manipulate the environment, or produce substances.
Zoan - Pretty simple here, Zoan types affect the user and make them able to turn into animals and use the abilities of said animal.
Logia - The strongest and rarest of Fruits, Logia types are able to control elements. They are so powerful and hard to counter often times, Oda had to come up with an ability to counter them during Part II, called Haki, although he foreshadowed the ability even during East Blue.
Other than that, Devil Fruits are rather mysterious. Hell, we don't even know their origins, although Part II seems to be explaining some of our questions with the Smile Factory and whatnot.
