On the Roman side, you have the comedies of the author Plautus, which are actually adapted from Greek New Comedy. Greek New Comedy came around in the Hellenistic World, and was less of the raunchy fart jokes of Aristophanes (and is thus less fun), and more poking fun at social class. Menander is the only extant author we have of this type of comedy, but the Roman authors like Plautus translated some plays, and wrote others in the same tradition. These comedies are based on stock characters...the most popular of these is the "clever slave". My favorite of Plautus is Amphitryon, which mocks the parentage of Hercules...unfortunately, it's hard to find a good translation. Miles Gloriosus is also popular, and a fairly good translation is here.

Laughter in Rome was actually considered good luck in some instances, because it could divert the Evil Eye. For other instances of Roman laughter, check out satire in Juvenal and Martial. If you want to go earlier in the Greek world, there are a few lyric poets who make fun of people, such as Semonides.

I don't know about the eastern side of this, although I do know that tricksters such as those featured in the Chinese text Monkey were meant to be funny. It might at least give you a start for the east...wikipedia link here. It's a really fun read. Come to think of it, trickster tales from all sorts of cultures might help you...the book Trickster Makes This World.