Why does the Boeing 737 have a pitot tube on the tail?
There are five sets of pitot tubes on the 737, organized into two groups, the pitot tubes on the nose are used for airspeed measurements, independent for the pilot and copilot and one as a backup. There are two pitot tubes on the tail that are for the "elevator feel and centering unit" (pdf; page 8).


  The elevator feel computer provides simulated aerodynamic forces using airspeed (from the elevator pitot system) and stabilizer position. Feel is transmitted to the control columns by the elevator feel and centering unit.


The airspeed may not be the same due to shielding in high angle-of-attack situations. I do not believe that the airspeed from the pitot tubes in the tail is visible (or useful) to the pilots. There is a warning that appears in the cockpit when the sensor fails.