Apples

Apples are Ryuk's favorite food and the only thing he is seen eating. He likes apples from the human world because he finds them "juicy" and stated that they are an addiction for him, like alcohol or cigarettes for humans. He has only been seen eating red apples (likely fuji apples). Ryuk exhibits symptoms of withdrawal if he goes without; these symptoms include contorting his body into uncomfortable positions and desperation to the point that he will take orders for one (i.e. looking for hidden cameras in Light's room).

Shinigami apples
Apples from the Shinigami Realm look like shriveled green peppers, are black or maroon in color and don't resemble their human counterparts. Misa gave a juicy human apple to Ryuk, and in return, he lets Misa have a bite of an apple from the Shinigami realm that he was carrying with him at the time. Misa takes a bite and then spits it out in disgust, saying that it "tastes like sand."

Apples eventually become a popular commodity/currency in the Shinigami Realm. In the C-Kira one-shot, Midora bribes the King of Death with 13 apples she brought back from the human world in order to receive an extra Death Note that she gives to C-Kira.

Gukku, one of the first Shinigami seen in the series, comments in the one-shot that Ryuk bringing human apples to the Shinigami Realm is the reason why Death Notes became so easily available. Gukku also states that "he doesn't know if that's a good thing or not."

Trivia

 * Ohba has stated in an interview for Death Note 13: How to Read that he chose apples because he thought they looked "cool" when contrasted with Ryuk's black figure.