It would be impossible not to place this film on the top of my list. The perfect situational comedy (Groucho marx the anarchical leader of a country!), more great jokes (almost all of them by Groucho in no less than 5 minutes) than pretty much the rest of the films on the list combined, and not one wasted minute of subplot (arguably the single greatest thing about this film). "If you think this country's bad off now, just wait 'til I get through with it!"
This might be the most artistic comedy ever made, with every gag accomplished to perfect precision. The finesse of this comedy is even more remarkable given the fact that it was made during an era when overreaction and melodrama ruled. But of course, we all know why - it was Buster Keaton's reaction to the comedy, he was merely an inactive spectator experiencing the result of what was happening around him unsympathetically, he was not really an active participant in the comedy (merely a spectator - and that's why we love him).
Probably the most underrated comedy in history, Arsenic and Old Lace is not only the apex of Cary's talents as an acrobatic, fast-talking comedian but of the screwball comedy genre as a whole. The dull moments in this film are few and wholly forgivable given the superb, fast-paced nature of the raucous comedy. "Aunt Martha, there's a body in the window seat!"
While not nearly as pure as their masterpiece "Duck Soup," the Marx Brothers are still at the top of their game in this fantastic comedy that paces itself far more gently than is necessary. "Is my Aunt Minnie in here?" "I don't know. You can come in and prowl around if you wanna. If she's not in here, you can probably find somebody just as good!"
No list of the greatest comedies would be complete without this comic gem starring Bill Murray in an absolutely showstopping performance as Bob Wiley, a maniac who pretends to have extreme mental issues so that he won't actually have them (?). Richard Dreyfuss is almost as good but not quite. You can't go wrong with this riot.
Some of these films make the list because of their GREATNESS as a comedy (such as Dr. Strangelove) rather than how many laughs it gets. Still, regarding on your taste and intellect, Dr. Strangelove might get as many laughs as Duck Soup (a fireworks show of belly laughs).