What’s the difference between a bison and a buffalo?
[Australian] You cahn’t wash yer fice in a buffalo!
An Australian was hiking in New Zealand when he saw a local having sex with a sheep. ‘Where I come from we shear those!’ To which the Kiwi replied, ‘I’m not shearing. Get your own!’
Hey señor, what do you geet when you goose a ghost?
A handful of sheet!
Q: Where do cousins come from?
A: An aunt hole!
It would have to be told by/heard by someone who pronounces aunt “ant”.
A Mexican student in elementary school was asked to use the colors pink, green, and yellow in a sentence.
"The phone goes “green, green”, I pink it up, and say, “yellow”.
Why’s it so difficult to make a phone call in China?
Every time you Wing, you get the Wong numba.
Funnier if the listener (and optionally the speaker) is of Southern extraction:
Q: How do you catch a polar bear?
A: Cut a hole in the ice, catch a fish, and leave it next to the hole. When the bear comes up to get the fish, you kick him in the ice hole.
The Italian Who Went to New York (Sonna Ma Bitch!)
…and, of course, the one about the hollow estatue
It’s well known that polar bears are partial to peas. So sprinkle peas around the hole. When the bear comes to take a pea, you kick him in the ice hole.
This depends not so much on accent as such, but more on local pronunciation (and also local slang). It won’t work for Americans:
Two farmers having a yarn:
“Goin’ to Sydney, mate?”
“Yeah…”
“What route ya takin’?”
“Aaah… thought I’d take the missus. After all, she stuck by me through the drought.”
And Johnny, that first joke only works for badly done Hollywood “Australian accents”. 
Scottish accent
What’s the difference between Bing Crosby and Walt Disney?
Bing sings but Walt Disney.
A young guy joins the air force, wanting to fight for his country. The first time he gets into a plane, he flies it perfectly, doing banks, loops, etc. So the man training the recruits asks him,
"Have you ever flown a plane before, young man?
To which he replies, “No sir, I have not.”
Despite this, it is obvious that the man is very talented, so he is immediately stationed aboard an aircraft carrier in the Pacific. Once again, on his first day he takes off and flies like an ace pilot. He shoots down a number of enemy planes, and manages to avoid being shot himself. Finally, he decides it’s time to land, so he lands on the aircraft carrier below him. When he lands, he jumps out of the plane and runs up to the officer on deck.
“Did’ya see that? I shot down all the enemy planes on my first day!”
To which the officer replies,
[Japanese accent] “Ah, but you make one very serious mistake.”
ROR!
A young lady is living alone in her very first apartment. The phone rings. She picks it up and a voice on the other end says “I am the viper.” She hangs up, kind of skeeved out, but she thinks, well, weird things happen.
The next day, the phone rings again. “I am the viper.” Well, now she’s getting a little worried.
The third day, again with the phone. “I am the viper.” She locks her door.
The fourth day, the doorbell rings. She opens it to find a tiny little man. He says. “I am the viper!” She screams and slams the door.
He yells through the door, “I come to vipe your vindows!”
A woman takes an antique clock to a German clockmaker to be repaired.
“Vot is ze matter vith ze clock?”
"Well, it used to go “tick tock tick tock”, but lately it’s just been going, “tick… tick… tick…”
The old man looked at the clock and addressing it directly, said, “Ve have vays of making you tock!”
The chinese virgin bride in preparing to go on her honeymoon asks her friend for advice on sexual positions and preferences so she will be ready.
On their first honeymoon night the couple are getting ready to consumate the marriage.
The husband asks “You ready make love now?”
The wife responds “Yes.”
The husband follows up with “How you like make love?”
She answers “I like the sixty-nine.”
The husband looks completely puzzled and befuddled and asks:
“You want the beef and broccoli?”
Somehow, an orange tree was growing in the north east of Scotland and bearing fruit. One day one of the oranges was feeling sleepy and dozed off, up on the branch along with all his other orange chums. He slept for a few hours, and when he woke up he saw that he was alone, all his mates were lying on the grass surrounding the tree.
This came as a surprise, so he said,
“Jaffa?”*
*Should be said with a long 2nd syllable. It is actually the north east pronounciation of “Did you all fall?”
“Bisexual:” what a Southern prostitute says.
Ja. Und ze Fokker vas flying a Messerschmidt.
Tortuous pun I once heard on NPR. The accent is upper-class British.
I’ll make it as short as I can because I think it’s worth it.
It seems a poor boy from the village somehow became enamored of the local squire’s daughter. She did not return his affections, and told him as much, but eventually she did invite him up to the manor to meet her parents.
She told the boy that her family were nudists, so he should remove his clothes before joining them on the back terrace. He did so. Of course she was lying to humiliate him, and when he walked out in the altogether, everyone else was clothed.
Moral: Never undress to meet the Pa of a woman.