I'm trying to come up with a good list of a subset of workplace comedies, the military sitcom. This is what I have so far:

Broadside
CPO Sharkey
Ensign O'Toole
F Troop
Gomer Pyle
Hogan's Heroes
I Dream of Jeannie
Major Dad
MASH
Mchale's Navy
Phil Silvers Show
Private Benjamin

UK:
Blackadder Goes Forth
Dad's Army

Obviously, a lot of sitcoms touch the miltary at some point or other, but I'm looking for ones that mainly revolved around the military. I'd say Major Dad and I Dream of Jeannie are probably borderline, but included them because the main character is usually in uniform.

What are some others?

"Major Dad" is a great, very underrated show.

"Enlisted" which was more recent.

M*A*S*H, of course, could sometimes be quite dramatic

I think one of the first must have been that live sitcom, "The Soldiers," from the summer of 1955, and starring Tom D'Andrea (from Life of Riley) and Hal March. It pre-dated even "Bilko," which didn't make it's debut until the fall of that year.

There were also some of those military sitcoms of the 1960s which were based on more successful feature films, like "Mr. Roberts" starring Roger Smith, and that hour-long adventure-comedy "Wackiest Ship in the Army.". Both were aired in that same 1965-66 season. Also, what about that tv-version of "No Time for Sergeants," starring Sammy Jackson? And "Hennesey" with Jackie Cooper was more successful than all of those, lasting a full three seasons (1959-62). That one really needs to be run again.

"Operation Petticoat" (1977 - 1979). First time I saw Jamie Lee Curtis.
Agree about "Hennesey".

The Many Loves of Dobie Gillis is worth a mention -- became a military sitcom when Dobie went into the army for a long stretch.

"McKeever & the Colonel" (1962 - 1963) at Westfield, a military academy.