Why does the US President fly in an obsolete 747-200?
The 747-200 derivatives used for transporting the President of the United States are VC-25's operated and maintained by the United States Air Force. The US Air Force tends to keep planes for a long time, as they still operate 707 and B-52 aircraft twice as old as these 747's. The E-4 aircraft, also based on the 747-200, have been in service for 40 years. The reasons for keeping the VC-25 aircraft flying are similar to these other examples.

A lot of work went into the VC-25 aircraft. They have been modified to add aerial refueling capability, defensive mechanisms, and include extensive additional electronic equipment for communications. Installing the special interiors was also a major task. As with a bomber or AWACS, there is a large initial investment in development to design the systems and build the aircraft. Upgrading components and providing proper maintenance allows these aircraft to perform their missions long after their entry into service.

Another difference is the engines. The 747-200B model has GE CF6-50E2 engines producing 52,500 lbf thrust each. The VC-25 aircraft have newer CF6-80C2B1 engines producing 56,700 lbf thrust each, which is the same engine as the 747-300. Newer engines go a long way towards improved performance.

As DeltaLima notes, these aircraft do not spend nearly as much time in the air as commercial aircraft. Yet there are many commercial aircraft in service with similar or greater age, including some 747-200 aircraft.