The University of Wolverhampton published a list of the world's oldest jokes, and the oldest one they listed was a Sumerian fart joke. This joke was dated to about 1900 BC. The joke is #15-16 at the electronic compilation of Sumerian literature hosted by the University of Oxford (http://etcsl.orinst.ox.ac.uk/proverbs/t.6.1.01.html) and you can read a BBC News story about it here: http://news.bbc.co.uk/2/hi/7536918.stm.
The joke is: "Something which has never occurred since time immemorial; a young woman did not fart in her husband's lap." I suppose we've lost a little something in translation.
The Iliad has some humorous scenes, so this is a good place to start.
And the Odyssey, though this is said to be later than the Iliad.
hi! fyi, you'll find more on the oldest joke, and lots of other examples from the ancient world in the FAQ