For me, cleverness is probably the most important element of comedy.
Word play and surprise and crafty story-telling are each elements in "being clever" and are all opposed by obvious jokes, unimaginative insults and sexual innuendo.
Since this question is an opinion question, all answers will be different. In terms of comedy, some of the best comedies that I have ever read come from the comedies of Plautus, a Roman poet, of the second century A.D. His comedies are creative reworks of original Greek comedies and there are a few elements in his poetry that make him very funny and powerful.
First, there are may role reversal. Slaves overcome masters. Men are afraid of women. Sons outwit fathers and foreigns conquer Romans. These reversal are a breath of fresh air, because the underdogs from an ancient point of view get the upper hand.
Second, I think these reversal are also powerful, because they tell us where social anxieties are. It gives us a window into the lives of people.