The oldest joke book in existence, Philogelos, is a Roman book written about the 4th century AD around the time of Constantine the Great (in Greek). The book is mostly quips from two guys, Hierokles and Philagrios, about whom little is known.
Like modern comedy, Roman comedy at the time of Constantine was based on the fortunes and foibles of a gallery of stock characters: the drunk, the miser, the braggart, the sex-starved woman, as well as a classic type known as the Scholasticus, variously translated as "pedant," "absent-minded professor," or "egghead."
There's a great video here, in which Brit comedic legend Jim Bowen does ancient Roman material from Philogelos in a modern comedy club.
- Scholasticus meeting a friend exclaims, "Why, I heard you were dead!" The other replies, "Well, I tell you that I'm alive". "Yes," persists Scholasticus, "but the man who told me so is more truthful than you!"
- A son says to his father, "Base man! Don't you see how you have wronged me? If you had never been born and stood in the way I should have come into all my grandfather's money."
- An Abderite saw a eunuch talking with a woman and asked him if she was his wife. When he replied that eunuchs can't have wives, the Abderite asked: "So is she your daughter?"
Ok, so these aren't exactly knee slappers to our modern ears. Some of the jokes are no longer understandable as funny because of differences in customs and lifestyle. For instance there's a lot of jokes about lettuce. Fourth century Romans loved lettuce jokes because they evidently were dirty jokes (???).
- An intellectual was eating dinner with his father. On the table was a large lettuce with many succulent shoots. The intellectual suggested: "Father, you eat the children; I'll take mother."
Well, maybe not much has really changed in 1600 years.