Why?

Removing the rear seat significantly increases the cargo space, which opens up new mission possibilities. For example, I can normally fit 1 bicycle in the back of the plane, but with the rear seat removed I can fit 2 bicycles. This makes it possible to take a friend and make cross-country trips to explore some of the best bicycling across the pacific northwest.

Regulations

For my 1980 172 (built in 1979), the POH equipment list does not mark the rear seat as required, so the airplane is airworthy with, or without, the rear seat. But can a pilot remove the rear seat himself? FAA regulations part 91 section 43 governs the maintenance pilots can perform. Appendix A, (c) says:

(c) Preventive maintenance. Preventive maintenance is limited to the following work, provided it does not involve complex assembly operations: 
...
(15) Replacing seats or seat parts with replacement parts approved for the aircraft, not involving disassembly of any primary structure or operating system.

The rear seat comes out with 4 simple bolts and nothing has to be disassembled. To get the rear seat out of the airplane one of the front seats has to be removed, then reinstalled. This can be done without any tools at all.

Conclusion: it is legal to fly the airplane without the rear seat, and it is legal for a pilot to remove and install it.

Of course, this changes the weight & balance. So the pilot removing/replacing the seat must note the removal/replacement in the airframe logs, citing the above paragraph as his authority and the maintenance manual as his reference. Also use the weight/arm info from the equipment list to make appropriate modifications to the empty weight/arm of the aircraft in his W&B computations for flights with the seat removed. And, of course, the pilot would have to be sure that at most only two people were in the plane when it is being operated.

How-To

So now that we know it’s legal, how do we actually do it? It turns out to be quick and easy.

Before you start it looks like this:

Step 1: remove one of the front seats

This makes room to remove the rear seat from the airplane, and you can reinstall it afterward. I removed the right / co-pilot seat.