How do you shoot a blue elephant?
with a blue elephant gun
How do you shoot a red elephant?
you hold his trunk shut until he turns blue, then shoot him with a blue elephant gun
Or my daughter’s favorite:
Why did the boy throw the clock?
he wanted to see time crash!
What is the smallest room in the house
A mushroom
(The favorite joke of the 7 year old son of my former boss)
Yeahbut would you tell this joke to a Seven-year-old? 
I got both jokes, too. Guilty as charged…
A series of really clean “riddles.” Mental age required – roughly 4.78:
Q. How do you catch a fish using a clock and a hammer?
A. Wait until the curious fish comes up to see what time it is, then bonk it on the head with the hammer!
Q. How do you catch an elephant using a telescope, a matchbox and a pair of tweezers?
A. Look at the elephant through the “wrong” end of the telescope. Pick up the tiny elephant with the tweezers and put it in the matchbox.
A “can’t win” riddle:
Q. Is a Crocodile longer or greener?
A1. Hmmm… greener? Q1. But – it’s also long on the inside
A2. Hmmm… longer? Q2. but – it’s green cross-wise, too!
Q. Everybody knows Red Elephants are really easy to catch, but White elephants are really difficult to catch. How do you catch a White Elephant?
A. Find a White Elephant. Tell it these stupid riddles. By the time you’re finished it will be red with irritation. And, hey, Red Elephants are really easy to catch!
Thankyouthankyouthankyou, i’ll be here all day! try the fish
One more – since this thread has been shot to hell already Censorship-wise – a technically “clean” joke (but which you wouldn’t tell a child or an older person either). I’ll put it in a spoiler on the off chance the original spirit of the thread will ever be revived…
10th grade Biology Teacher: “Students, which body organ is capable of growing to seven times its original size?”
Janet: (turns livid) “Teacher, I really must object to this kind of question in class!”
Teacher: “Johnny?”
Johnny: “In the human eye, the Pupil will expand up to seven times its normal size under low-light conditions.”
Teacher: “Johhny, this is correct. And Janet – you are in for a big disappointment…”
errrm,I see…um NOT offensive ,interesting little problem that one …
What’s black and white and red all over?
A nun chewing razor blades.
Did you hear about the magic tractor?
It drove down a lane and turned into a field.
How many men does it take to wallpaper a room?
It depends how thinly you slice them.
Why do pirates work in polar co-ordinates?
So they can differentiate with respect to aaarrgh!
A man was walking down a trail one day when he passed a small shrub. As he passed, he heard a faint “psst” emanating from under the shrub. He looked down and saw a snake, hiding amongst the leaf litter.
The snake warily introduced himself in perfect but accented English. The man, taken aback by a talking snake, immediately suspected foul play. The snake, who we will refer to as Sam, in an attempt to convince the man that he really was a talking snake, offered to answer any question that the man chose to ask.
Dumbstruck by the turn of events, the man asked “what is four times two?”.
Sam replied “before I answer this, I need you to go and find some sticks for me”. The man dutifully retrieved some sticks and placed them down in front of Sam. After a brief pause, Sam replied “eight”.
Bamboozled by the whole experience, the man asked why the sticks were necessary. Sam replied “well, you see, I’m an adder and adders need logs to multiply”, and with that, both went their separate ways.
I printed this joke before reading it and showed it to my wife. She died laughing. I’m afraid to look at it myself for fear of the same. This should be registered as a weapon or something!
Two bullets got married. What did they have?
a B.B.
Two drums and a cymbal fall out of a window… ba dum pssht!
What goes “ha ha ha ha… thud”?
A guy laughing his head off.
What do you call cheese that’s not yours?
Nacho cheese.
Well, if we’re doing some absurd exchanges, here’s one that I read that (so it said) every Jewish child has heard in one form or another:
Grandfather asks grandson: “What’s wet, green, hangs on a wall, and whistles?”
Grandson (thinks a long time, then): “Okay, I give up.”
Grandfather: “A herring.”
Grandson: “…?! But a herring doesn’t hang on the wall!”
GF: “So hang it there.”
GS: “Herrings aren’t green!”
GF: “So you paint it.”
GS: “But if it’s hanging on a wall, it wouldn’t be wet!”
GF: “It would be if you just painted it!”
GS: (exasperated) “But herrings don’t whistle!!”
GF: “Ah yes, I put that in to make it hard.”
One for the kiddies, only really works orally.
Q: Why is 6 afraid of 7?
A: Because 7 8 9.
How do you tell a boy chromosome from a girl chromosome?
You pull down its little genes!
Knock knock.
Who’s there?
The interrupting coefficient of friction!
The interrupting coefficient of friction w…
MU!!
Errr… that there herring sure looked red to me until you went ahead and painted it green! 
What’s a foot long and slippery?
A slipper.
Here’s one from my childhood that I still love to tell.
A man was building a house, and he decided to put in a fireplace. He drew up the plans himself, and calculated exactly how many bricks he’d need to build it. His calculations were perfect, right down to the last brick.
He then went down to Brick World and bought exactly that number of bricks. He brought them home and built his chimney. Thing was, though, that he had a brick left over. He looked at his receipt, he looked at his plans, but he just couldn’t figure it out. He could not account for the extra brick.
So…
…he threw it out the window!
Cracks me up every time.
What’s red and green and goes round and round a hundred miles an hour?
A frog in a blender
Knock, knock!
Who’s there?
Boo
Boo, who?
Don’t cry! It’s only a joke!
What do you get when you cross an elephant with a rhinocerous?
Eleph-ino
How do you capture a unique rabbit?
Unique up on them.
How do you capture a tame rabbit?
Tame way!
My six year old daughter loves this one though it could be considered offensive.
Why did Tigger look in the toilet?
He was trying to find Pooh!
Knock-knock
Who’s there?
Dwayne
Dwayne who?
Dwayne the tub, I’m dwowning!
If it’s truly kids’ jokes you want…
Um… there was, um, this, um, chicken? And there was this, um, road? And, and, and, the chicken? He, um, walked across the road? Yeah. And then he was, um, on the side of the road, but the other one? Yeah.
I’m not sure why.
Can I have a peannabunna sammich?
Knock knock,
Who’s there?
Matthew
Matthew who?
Matthew-lace came untied.
…
…
Sam and Janet who?
Sam and Janet evening.
…
…
Little old lady who?
I didn’t know you could yodel.
…
…
Osborne who?
Osborne in Winnipeg.
Don’t get me started on “no arms/no legs” jokes.
I cannot tell you how disappointed I am that Neil Gaiman didn’t, in fact, make up the herring joke. (It’s in MirrorMask.) 
No offense to anyone- legitimate question re something I must be missing, because many do it- why spolier boxes with jokes? I can see with key movie plot points, but why jokes? Is there ever a time one would want to know the set-up to a joke but not the punchline?