Do US military aircraft have tail numbers beginning with "N"?
The 'N' numbers you're referring to are FAA registration numbers. The FARs (Federal Aviation Regulations) specifically mention registration as not being required for military aircraft:

14 CFR 47.3


  (b) No person may operate an aircraft that is eligible for registration under 49 U.S.C. 44101-44104, unless the aircraft—  
  
  (1) Has been registered by its owner;  
  
  (2) Is carrying aboard the temporary authorization required by §47.31(c); or 
  
  (3) Is an aircraft of the Armed Forces


The FAA issues these registrations in accordance with its responsibilities under the Chicago Convention on International Civil Aviation, which required (in Article 20) that:


  Every aircraft engaged in international air navigation shall bear its appropriate nationality and registration marks.


As per the above-cited 14 CFR 47.3, though, the U.S. specifically requires that all eligible aircraft have registrations unless it's either a military aircraft or it has temporary authorization under 14 CFR 47.31(c).