The world's funniest joke was the "Gooseberry Joke" as told by the Dangerous Brothers.
The Dangerous Brothers, when they existed, were a very young Rik Mayall and partner Ade Edmondson. This was before the Young Ones (where they teamed up with the Outer Limits - Nigel Planer and Peter Richardson, except Peter pulled out) and before "Bottom" where R&A acted as the Dangerous Brothers (same clothes, same persona) except they hit each other in a televisual way with frying pans and pots etc.
On stage the Rik character would start the joke innocently asking what's green and hairy and goes up and down? (the answer's a gooseberry in a lift. Hee hee) Ade's character was puzzled on several counts (not the least of them being an absence of humour). He asked how Rik knew. Then he asked how the gooseberry operated the lift. Then who told Rik. For about 20 minutes Rik continually tries to adapt the joke, adding Ade's riders in order to make sense. It turns out that Rik actaully KNEW the gooseberry, and his name was Derek.
As you're probably aware by now, the joke was a lot funnier than any attempt at explanation. It's probably on YouTube.