I like anti-humor.

I don't think this is on the level of The Aristocrats (very NSFW) but I like it:

A horse walks into a bar.
The bartender says "why the long face?"
The horse replies "I'm an alcoholic."

I also like jokes that involve turning the listener into the straight man. At work, when we're fiddling with some computer issue or problem - I love to say - "it looks a bit like a henweigh" Of course they reply - "what's a henweigh?" and I get to say "about 4 pounds". Childish? Yes - but it gives me a thrill. Very similar to the Dickfer joke in Spies like us.

I also like what is supposedly the shortest joke in the world:

"Pretentious? Moi?"

On long trips with the family we have joke contests. We have 2 minutes to think up an original joke and then it's judged- with the winner getting to judge the next round. According to my kids, this is the best joke I've ever made up:

What do you call a cowboy dinosaur who falls off his horse?
WhyImaSoreAssTex.

No, I won't be quitting my day job anytime soon.