Yes, most military aircraft, including fighter aircraft, are equipped with a "black box" called flight data recorder (FDR) / crash survivable memory unit (CSMU) / integrated monitoring and recording system (IMRS) / deployable flight incident recorder set (DFIRS).

Sources [1, ( B-1B, F-22, T-45, B-2, F-4, F-15, F-16, C-5 Galaxy, NATO AWACS, and the Space Shuttle)][1]
[2. (F-18, floating black box)][2] 


  [1]: http://www.armedforces-int.com/article/flight-data-recorders-crash-survivable-memory-units-tactical-military-aircraft.html
  [2]: http://www.defensemedianetwork.com/stories/%E2%80%9Cdfirs-phone-home%E2%80%9D/