Writing Comedy by John Byrne has a good section on different types of jokes. They include:
Literal and multiple meanings, e.g;
'I've got one deaf ear, I found it on the floor of a barbershop in Glasgow.'
Seeing a word and then using it in a different context.
'I just came back from the sheepdog trials, three sheepdogs were found guilty.'
Using words such as 'for' or 'on' or 'before' to trick the reader; e.g;
'What's Nat West short for? They ran out of money.'
'Do you agree with sex before marriage? Not if it holds up the ceremony.'
Double entendres:
'I'd like to buy some deoderant, please.'
'The ball type?'
'No, it's for under my arms'.
Backwards Writing:
'Have you heard the joke about the doomsday cult? No, oh well, it's not the end of the world.'
Telling the truth:
'The World Food Summit. That's where all the world leaders get together to discuss solutions to global poverty and starvation. And then go for a really good meal.'
Confirmations and contradictions:
'The Archbishop of Canterbury says horoscopes are just supernatural mumbo-jumbo.
He's bound to be sceptical - he's a Taurus.'
Using common cliches or phrases:
'I spent £80 on a tattoo on my left arm and £80 on a tattoo on my right arm as I wanted to balance transfers.'
And of course puns:
'What do you call a stupid gypsy? A retarred.'