M*A*S*H the series began in 1972, it follows the life of Dr. Benjamin "Hawkeye" Pierce who was drafted into the Korean War. He's a civilian at heart and makes it known by word and deed, he ignores military discipline and acts crazy to stay sane in a place he doesn't want to be.
Other characters are Lt. Colonel Henry Blake who is about as un-G. I as you can get, and often sides with Hawkeye. "Trapper" John McIntyre is Hawkeye's sidekick. They often pull pranks on their nemesis Major Frank Burns, who is a semi-competent surgeon, and way too G. I. His sidekick is Major Margaret "Hot Lips" Houlihan, whom Burns is having an affair with that only he and Hot lips think is secret.
Other characters are Corporal Klinger, who dresses in women's clothes to try and get out of the army on a section 8, and Father Mulcahy.
The show does take a more serious tone in its later years (it lasted 11 seasons), it sometimes interferes with the humor and does dip a little in quality (which is why I did not give it a 10), but it does still have many funny moments throughout the series.
The show also has multiple characters who exit the show and are replaced with other very different characters. These changes are handled very well, and don't try to mimic the departing character.
For those who have never seen the show (I had not seen it until 2 years ago) I highly recommend that you see it from the beginning.