It’s been a long time since I heard (much less told):
Q: What goes in hard and good and comes out slick and slimy?
I’m so old I remember when “harass” was two words. 
Are you my 8th-grade history teacher? He used to tell horrible Polack jokes, only his protagonists were “Ethnickians.” Hardy har har.
I thought it was “What’s pink and hard when it goes in, and soft and wet when it comes out?”
Bubblegum
Not sure why that’s obsolete, though.
Given that my wife’s Polish, the only Polish joke I get to tell any more is the good one, about the Mongols.
Q. What do you get when you stick a finger in the president’s ear?
A. Johnson’s Wax.
(Funny as hell in 1965).
Here’s one that’s truly obsolete, and would have only made sense to Bostonians in the first place:
A man is standing by the side of the road, bent over in obvious pain. He hails a taxi, and as he crawls in, the driver asks, “The Peter Bent?” And the man replies, “Bent hell, she bit it clean off!”
Only locals of a certain vintage would recognize the Peter Bent as the Peter Bent Brigham Hospital.
Did you know that the first girl killed in Jaws had dandruff? Yup, they found her Head and Shoulders on the beach.
A joke from the Branch Davidian standoff in Waco, Texas:
What does Waco stand for?
- We All Cooked Ourselves
or
- We Ain’t Coming Out
And this one following the Space Shuttle explosion in 1986:
What does NASA stand for?
Need Another Seven Astronauts
As for Polock jokes, these were supplanted by blonde jokes; same premise, different target.
A joke I heard on the British version of The Office that will someday be obsolete:
What’s black and slides down Nelson’s Column?
Winnie Mandela
How do you tell an Italian tank?
It’s got one forward gear and four reverse ones.
Oh, the Polack jokes are still around, they’ve just become, depending where you live, Hoosier jokes, Kentuckian jokes, Aggie jokes, or maybe Newfie jokes. I’ve heard several of the same ones with all those distinctions. I’m quite fond of the Cheerios one.
How many Doctor Who fans does it take to change a lightbulb?
none - they just sit around wishing it would come back on.
How many Star Trek fans does it take to change a light bulb?
One to change it, and two to argue about whether the new one is as good as the old.
The first joke is obsolete because Doctor Who has come back on. The second is obsolete because there are now more than two versions of Star Trek. But they were both funny back in the day.
What’s the opposite of Christopher Reeve?
Christopher Walkin
Princess Grace was on the radio.
On the radio, on the dashboard, on the steering wheel…
(I recycled that one for Princess Diana.)
:smack: Walken!
I remember a reprint from an (I think) early '60s issue of Mad: David Berg’s “The Lighter Side of Women.” In one strip, a woman tells the pharmacist “I have this terribly important prescription I want you to fill! And while I’m here . . .” names a long shopping list of cosmetics, nylons, etc. He gathers them all, presents her order and price, which totals out to more than she’s got on her. “Oh, dear! In that case, forget the prescription!”
Triply obsolete: Because of the sexism, and because nowadays you wouldn’t ask a pharmacist to assemble all those purchases, and because she can get the prescription without waiting!
I remember that from one of Larry Gonick’s ethnic joke books from the '70s, and I alwas wondered what stereotype it was based on – until I read one of Isaac Asimov’s popular histories, describing how the performance of Mussolini’s troops in WWII was so inept it provided one of the few notes of comic relief.
Have you heard about Ranch Davidian salad dressing? You squeeze and you squeeze but it just won’t come out!
Why can’t Helen Keller have babies?
Because . . .
She’s dead!
What’s the difference between Dan Quayle and Jane Fonda?
Jane Fonda went to Vietnam!
Well, it seemed funny in 1988 . . . before we had Bill and W . . .