What is this thing between the engines on the F-14 Tomcat?
This is the line for dumping fuel in an emergency. If the F-14 needs to land quickly but is too heavy for landing, fuel can be pumped overboard through this pipe. To the left of it is an antenna, and the rod below the fuselage is the arrestor hook.

The Australian F-111s use the same arrangement to great effect during flight displays.

From the F-14 Walk-Around Photo Index Page:




  Back end of the "beaver tail".  The red hole is the fuel dump point.
  The beige item is the rear ALQ-126 antenna, paired to the ones on the
  wing glove area.  This antenna, like the forward ones, was introduced
  with block 110 F-14As and all subsequent aircraft.  Also visible is
  the hook portion of the arresting hook.