You can freeze cheese. While hard cheeses freeze fairly well, soft cheeses, such as ricotta or cream cheese, do not. Even hard cheese is likely to change in consistency when frozen.
According to About.com, it's best to freeze cheese inside a freezer bag or in its original packaging. Eat By Date points out that the firmer the cheese, the more likely it is to freeze successfully. Frozen and thawed firm cheese, however, is likely to become crumbly and therefore is best used in cooking. Soft cheeses tend to become grainy, crumbly and runny when frozen and thawed. It is best to thaw frozen cheese in the refrigerator rather than at room temperature, and it is advisable to use the cheese within three days of thawing.