Comedy is one of the oldest genres of film. Its earliest go all the way back to ancient Greece, although the classical definition of a Greek comedy differs somewhat from what we have today. Most Greek comedy did not rely on ribald humor so much and might fit more readily into the drama section of your local video store.
It wasn't until the late 1920s that sound was introduced to moviegoers, greatly broadening the scope of comedic cinema. This allowed for all sorts of deeper plots and witty dialogue. The Marx brothers' "Duck Soup" is a favorite from this era, as is Laurel and Hardy's "Way Out West". The Three Stooges were also among this era's most popular entertainers.
The 1950s saw another major change in the cinema business as the television started rising in popularity. The short films of earlier years were largely shifted to the T.V. set and cinema started focusing more on feature-length films. The 50s and 60s gave us screwball classics like "The Nutty Professor," "It's a Mad, Mad, Mad, Mad World," and "The Pink Panther." This era also saw movies with more adult themes and a number of darker films like "Dr. Strangelove."
The 70s and 80s were good years for comedy, for Mel Brooks if nothing else. These decades also gave us Monty Python, as well as a whole slew of hilarious films from various "Saturday Night Live" cast members. "Ghostbusters" and "National Lampoon's Vacation" are not to be missed.