Coming to America is a great comedy. Some of my other favorites from the '80s, in no particular order:
Airplane!
Beverly Hills Cop
Bachelor Party
Trading Places
Stripes
National Lampoon's Vacation
National Lampoon's Christmas Vacation
Revenge of the Nerds
Sixteen Candles
Fast Times at Ridgemont High
The Breakfast Club
History of the World, Part I
Ferris Bueller's Day Off
Another classic is 48 Hrs. It is not really a comedy, per se, but with Eddie Murphy, there are plenty of hilarious scenes. The '80s was a great era for comedy.
Two movies I did not list above are Caddyshack and The Blues Brothers. Caddyshack is good, but the comedy is a bit zany at times. I tire of it. The Blues Brothers is also good, but not one of my favorites of the era.