Examples of current jokes I tell that fit the model. I'm not sure if it's an accident that all of these are pretty blue in one direction or another if told properly. Note that the joke may also depend on doing a good impersonation of some kind:
Norm MacDonald's Moth Joke
(My favorite joke ever)
The Deaf Jewish Dog Joke. Mighta been Woody Allen, mighta been MetaFilter I got it from... i guess I'll relate a rough text version: Two guys and a dog are sitting around when one guy says to the other, "Hey, did you know my dog is deaf and Jewish?"
"How do you know?" the other guys says.
"Watch," so the first guy picks up a tennis ball from in front of the dog and tosses it across the room. "Fetch, boy."
The dog sighs and gets up and says, "Oh with that ball, always you're throwing it and it's bouncing! I don't know what you want from me I'm old! Maybe if you fed me a little better, with better portions. I see you with the schmalz in there! And me with kibble! Is a walk to much to ask? Oy." And with that the dog wanders into the kitchen and flops down.
"Okay, so how do you know he's deaf?"
"He thought I said, 'kvetch.'"