This is what most people think of when hearing the word "patent." A utility patent involves something "useful" such as inventions in the electrical, chemical, mechanical, software, pharmaceutical, business method, and other fields. The term for a utility patent is 20 years after the patent's application date.
The design patent protects the ornamental aspects of an item. Essentially the design covers how the thing looks. The term for a design patent is 14 years after the issue date.
As the term plainly states, a plant patent covers a plant. More specifically, a plant patent protects asexually reproduced new plant varieties. The term for a plant patent is 20 years from the application date.