These are not necessarily the traditional type of war movies; I have included films that are set in wartime and for which a war is an important contemporaneous event ("home front" movies) and also movies for which a military setting is central (A Few Good Men, for example).
The following alphabetical list includes my star rating for each movie and the war involved. (NOTE: Dates covered are mid-1983 through 1996. I didn't start using stars until late 1989, so ratings for movies older than that have been added after the fact. Also, I did not write as many reviews as Siskel & Ebert. These are definitely NOT the only war movies, or the best war movies, to come out during this period; they're just the ones I have reviews for.)
COURAGE UNDER FIRE. Gulf War 
CRIMSON TIDE. Submarines; narrow aversion of nuclear war.
FEW GOOD MEN, A. Cold war, military justice. 
GARDENS OF STONE. Vietnam
GLORY. U.S. Civil War
GOOD MORNING, VIETNAM. Vietnam 
HUNT FOR RED OCTOBER, THE. Submarines; Cold War.
KILLING FIELDS, THE. Vietnam, Cambodia
MEMPHIS BELLE, THE. World War II
OFF LIMITS. Vietnam
OPERATION DUMBO DROP. Vietnam
SOLDIER'S STORY, A. World War II
UNDER FIRE. Nicaraguan civil war