Also called "maintenance fees", since December 12, 1980, all utility patents filed with the USPTO are subject to renewal fees. These fees are due 3.5, 5.5 and 11.5 years from the date of the patent grant. 
There are seperate fee schedules for patent-holders that can claim 'small-entity status' and late fees.  If a fee is not paid the patent expires after a six month grace period (and can only be paid up to six months in advance). However, a patent may be restored up to two years after the expiration of the grace period if the patent-holder can successfully claim that non-payment was unintentional or at any time until the end of the statutory term if non-payment was unavoidable.
Wikipedia claims that patents filed under the Patent Cooperation treaty are not subject to renewal fees. But the source does not back this claim.