Every single plane ever made has a design life limit.
Some of the design life limits are as follows:
747 20,000 cycles, 60,000 hours, or 20 years
767 no cylce limit, 100,000 hours, or 40 years
A300/310 36,000 cycles, 60,000 hours, or 20 years
L1011 115,000 cycles, 210,000 hours, or 20 years
DC10/10/30/40 42,000/30,000 cycles, 60,000 hours, or 20 years
The life limit of an airframe means that the airframe has been tested to these limits in simulation. Known issues found during testing have been dealt with and airworthiness directives issued. From what I understand the manufacturer must implement a maintenance program approved by the FAA to extend the life of the plane past the proven life limit.
The fleet leading planes in hours as of 07/99 are as follows: