I heard this the first time as a kid and just didn’t get it.
What do you call a Chinese woman with one arm and one leg?
Irene
I didn’t get that one for years, and then when I realized it was a racist joke, I was shocked. It makes me wonder if all the kids laughing at it knew what they were laughing for…and who they heard it from…
Two nuns are taking a bath. One says “Where’s the soap?”
The other replies “Doesn’t it?”
I heard this in a group of three people, and it took all of us plus the joke-teller’s explanation to get the pun involved. Not really worth the effort.
Where’s the soap? Okay now I don’t get it…help…
As for jokes I didn’t get at first…um…
I’ll get back to you on that one…
I don’t get that one either. I don’t mind being the bozo who asks “please explain”.
Also that one that’s in a sig here on the boards… something about a Discordian parrot pining for the fnords? I don’t get that one either, but I’m betting it’s REALLY CEREBRAL.
Not really! 
I’m going to deconstruct my sig, which will, as with all humor, completely destroy the joke, but that’s the kind of sacrifice I’m willing to make for the sake of my fellow Dopers.
Take one (1) Monty Python Dead Parrot sketch, which includes the lines “It’s a Norwegian Blue…'e’s pining for the fjords…”
Extract one (1) nonsense/mystery/buzzword from the Greater Church of Eris (Discordian), to wit, “fnord”
Combine said sketch and said buzzword and reveal…ta da!
It took me a really long time to get this, even after it was explained to me…
The first nun says “Where’s the soap?”, but the second nun hears “Wears the soap?”, to which she agrees. See, she thinks the first nun is using the soap for mastabatory purposes, and it’s wearing the soap down. So, she’s saying “[Masturbation with the soap] wears the soap”, or at least that’s what the other nun thinks…
Ah, got it. Thank you, thank you, jayjay and StephenG. Jayjay, far from destroying the joke, I now know an “in” that I didn’t know before. And that nun one would have taken me ages to figure out! It’s actually pretty funny.
Q: Why is Santa so fat?
A: He only comes once a year.
I heard this joke about 5 times before someone explained to me that come has 2 meanings.
Ooh, y’all are going to hate me for this one:
A couple of British tourists are mountain-climbing in the Rockies. They stop to admire a pair of majestic birds circling in the sky. Unfortunately they don’t notice the boulder rolling down the side of the mountain. They are killed instantly and their souls ascend into heaven.
As they pass the birds, one of the souls notices that they are in fact bald eagles. “Ah,” he remarks to his companion. “Eagles.”
But the eagles, who had been properly brought up, said nothing.
(You’ll know when you get it. Took me about two days.)
When I was growing up my dad told lots of jokes which I (and everyone else, usually) didn’t get and had to have explained. Some were better than others. Example: Two brothers were starting a ranch and were trying to find a name for it, so they called their father.
“That’s easy,” he said, “call it Focus”.
“OK,” they answered, “but why?”
“Because it’s where the sons raise meat.”
The next one is a true story (warning: potentially racially offensive material): Dad was working with some inner-city kids in some sort of sports program. He saw two boys sitting on the curb, one white and one black. The white boy picks his nose, holds out his finger and says “Wow, look at that booger!” The black boy responds, “Them’s not boogers, them’s G-men!”
When I was about four years old, my older brother gave me this riddle:
Q: How do you get down off an elephant?
A: You don’t. You get down off a goose.
I was confused. I didn’t get it. What did people at the circus do when they were done riding the elephants? Did they use the geese as stepladders? Wouldn’t that hurt the geese?
YEARS later, a friend of mine was wearing a new jacket. He said it had goosedown in it. Hmm… goose… down… AAARRGH!
A termite walks into a restaurant and asks “Is the bartender here?”
I don’t get the eagles one.
I think the point of the eagles one is that since the eagles are properly brought up, they don’t say anything if they have nothing nice to say, and thus don’t point out that the deceased tourists are British. (Mind you, there’s nothing wrong with being British as far as I’m concerned…)
Here’s one I sometimes tell that tends to mystify people for some reason:
Q. How do you steam a clam?
A. Make fun of its religion.
Nope, not quite. I was tempted to leave this one as an exercise for the reader, but that would be cruel. So here are some hints (more to come if needed):
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There’s a play on words involved. It works better when one of the words in question is spoken with a British accent.
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The eagles, as noted, don’t say anything if they have nothing nice to say.
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Think about what they would say if they were to respond in kind.
Heh, heh…
Eagles… eagles… 'ea gulls? Hmmm. Don’t know.
My very UserName is the one that caused me the most embarassment. Provided hours of enjoyment at a party one night:
I am Sofa King we Todd did.
Now, I believe my record speaks for itself.
Damn, now I’m going to be up all night trying to figure that one out…
Oh, wait! Does it have something to do with the fact that “Eagles” sounds vaguely like “Eh, girls” if spoken with just the right accent, suggesting that the eagles think the Brits are gay?
(BTW, I love the handle Fretful Porpentine… :D)
I get the one about the eagles, but…
I can make head nor tails of this one… 
Chinese accented english turns “l” into “r.” So “I lean” is pronounced “I rean” or “Irene.”
You aren’t all that Sofa King we Todd did.