Every commercial aircraft has a maximum number of cycles stamped on it by the manufacturer, technically known as the "Limits of Validity". This is because pressurization and depressurization do contribute to stress and fatigue -- and like (almost) everything in aviation those limits are conservative, some would say overly so. Nonetheless aircraft in the US tend to be retired (at least from commercial service with airlines you'd recognize) well before they hit the cycle limit.

For the 767-200/300 Boeing has that limit at 75,000 cycles or 150,000 flight hours (a -300F and -400ER is slightly more limited at 60,000 cycles or 150,000 flight hours) -- that's about 17 years of continuous flight. [See Boeing multi-operator message 10-0783-01B, December 19, 2010]

With a continuous airworthiness management program (CAMP) supervised by the FAA commercial airlines in the US generally maintain their aircraft better and more frequently than virtually any other piece of transportation equipment. Before NW merged with DL and retired their DC-9 fleet I had multiple rides on DC-9s that were at least as old as my mother, were older than the subject of this thread, and had I had no airworthiness concerns.