Visit letmegooglethatforyou.com, type in "how long do patents last," and click the Google Search button. Once the url is created scroll down below it and click "go." Then visit any one of the many sites that discusses when patents expire.
Patents last 20 years from the date of filing. However, a patent on a base concept will not prevent you from applying for a patent on improvements to the base concept. For example, the cell phones of today are filled with innovations not present in Bell's original telephone. A patent gives you the right to exclude others, but not a right to practice the invention. For example, you could exclude others from using your improvements, but still not practice your invention without a license from the patentee of the base concept. However, if your improvements represent a desirable area of expansion for the company owning the base patent, this type of situation usually works itself out as a business deal between the two companies to cross license patents or work together.
Heh, Daniel's answer was "ask Google." I'll answer your question. Patents do expire, generally about 20 years from date of filing. But just because a patent expires doesn't mean you can patent the same thing later.
First, it is important to know what kind of invention is being patented: an ornamental design or a process, functional machine, or composition of matter.
A patent on an ornamental design expires 14 years from the date of issue (not filing) in the United States. The ornamental design is not a functional, utility patent.
Generally, when a person talks about the patenting of an "idea," the invention relates to functional features or processes of an invention. These are protected by "utility patents" and have a term of 20 years from the date of filing in the United States.
Your "improvement" of a base design might be either an ornamental design or a functional improvement over the "prior art" base patent. In order to be patentable over the prior art, your improvement must be new, useful and nonobvious. Nonobviousness is an area of patent law that is beyond the scope of your question.
If you have a patentable improvement, you can file an application. Filing of a patent on an improvement does not infringe a base patent. Only when you or your licensee practices the improvement will it possibly infringe the claims of the base patent. The base patent will expire, and it is important to determine the expiration date. Assuming there are no other intervening patents, then you or your licensee may practice the improvement after expiration of the base patent, without fear of infringing the claims of the expired patent.
Utility patents can expire due to nonpayment of maintenance fees. This should always be checked.