I'll add my vote for Kelly's Heroes, but there are some others that come to mind, like M*A*S*H and Operation Petticoat.
The Hot Shots movies were certainly very funny. I particularly loved that movie Top Secret though, that was really funny.
The Hot Shots movies were hilarious, but mostly because of the Patton parody they made in Admiral/President Benson.
Well if the Holy Grail is class as a military comedy then the life of brian n the meaning of life shoud aswell cus they both contain a fair bit of military stuff (Monty Python Rock!!!!!, so my vote goes to the meaning of life)