It is possible for an inventor to categorize his idea or invention under one of three heads – utility patent, design patent, or plant patent. The clear definitions of these three main types of patents pre-empt any doubts whatsoever in determining the nature of the invention.
The most common type of patent is the utility patent. This kind of patent is awardable for an invention, or discovery, or an improvement thereof that can be applied, within reasonable time, for public good and / or makes sound economic sense.
Design patents are usually non-utility patents that are awardable to "new, original, and ornamental design for an article of manufacture".
Src: http://www.uspto.gov/web/patents/types.htm
Some special types of patents are those awarded for biological 'creations' and chemical items, business methods, software products. Details and links related to such and other issues can be looked up at http://en.wikipedia.org/wiki/Patent.