Harold and Maude.
Being There.
The Jerk.
And a few Woody Allen movies (e.g. Sleeper, Bananas).
For TV shows, I still love The Young Ones, though it was early 1980s (not sure if that qualifies as “older”).
Depending what side of the “Bang, Zoom” schism you fall on, The Honeymooners is still a good laugh for me. I’ve seen them all a bajillion times but Norton’s stable of po-lop-onies still makes me laugh without fail.
“Older” movies from the 1970s and 80s? Amateurs. 
My kids love Buster Keaton. We’ve seen several, and they have specifically requested to rewatch The General and Sherlock Jr more than once. These movies make my kids (currently 11 and 14) howl with laughter.
Chaplin, not so much. They find his sentimentality slow-paced, with big gaps between laughs.
Oh, and re the Hitchhiker’s books, my 14-year-old is reading them and loving them. She previously read the first one in a French translation, and then the second one in a German translation. (Artifacts of living in a multi-lingual country.) Then on a recent trip back to the U.S., she saw the five-book collected trilogy in a single volume, in English, and picked it up. She’s flying through them now. (She’s also read a bunch of Pratchett’s Discworld.)
For things that were released before I was born, I’ll go with The Three Stooges. I watched a few of their short episodes a couple of weeks ago, and they’re still hilarious. For sitcoms, I like Gilligan’s Island and Three’s Company.
For things that were I watched as they were released, the question is more clear cut. If I found them funny at the time, I still find them funny today. If I didn’t like them at the time, I still don’t like them today. I struggle to think of things which were good at the time but don’t hold up other than maybe children’s shows aimed at very young children. In other words, the question, at least as far as my tastes go, might as well be “what older works did you find funny when they were released”?
More of an admission that my youth was 40+ years ago 
Not to hijack, but I recently listened to it and “The Restaurant at the End of the Universe” on audiobook during a long road trip recently. I was absolutely flabbergasted at how different the experience was versus reading. I’d read those at least a couple of times before, and didn’t remember them as particularly dark or scary, but there were multiple places that surprised me as pretty dark or macabre.
FWIW, my 13 year old son loved them, and he mowed through my omnibus copy (print) of the whole series over the last few months.
As far as the OP is concerned, I saw “You Can’t Take it With You” a couple of years ago and was surprised at how funny it was, especially for a pre-WW2 Jimmy Stewart film.
Blues Brothers, Raising Arizona, Young Frankenstein, and Airplane! all hold up. My kids think they’re all funny, albeit in the TV-friendly versions. They also loved the Three Stooges when they were younger, along with Popeye the Sailor Man cartoons.
And in the category of “Wasn’t ever funny to adults, but still cracks young boys up.” Disney’s 1997 movie “Rocketman” with Harland Williams absolutely cracked my kids up, even 27 years on. I thought it was about as stupid at 52 as I did when I was 25.
I can’t believe how new a lot of these things are. I still find things funny from much farther back.
Mark Twain – A Connectiout Yankee in King Arthur’s Court and a lot of his short works. The man had a truly wicked sense of humor and means of expression.
Upon turning around from the Albert Memorial in London and seeing Albert Hall; It’s good to have more than one monument to oneself, to guard against accidents. I mean to have a collection of tombstones, myself.
On The Awful German Language: “When the literary German dives into a sentence, that’s the last you see of him until he emerges on the other side of the Atlantic with his verb in his mouth.”
The silent film comedies of Charlie Chaplin and Buster Keaton (and plenty of others). If you don’t laugh at Keaton’s The General, you have a heart of stone.
I still like the Marx brothers, especially their earlier films, up through at least A Night at the Opera
The Dick van Dyke Show still holds up wonderfully, and needs no excuses.
A Funny Thing Happened on the Way to the Forum
Who’s Minding the Mint?
And Now for Something Completely Different
Monty Python and the Holy Grail
I’ve been listening to the original radio broadcasts of late, and I’d forgotten just how crazily different each iteration of the story was. I kept waiting for the Hotblack Desiato scene that never came, and forgot about the Haggunenon owning the ship they steal.
I’m genuinely envious of your son being for able to read them for the first time with fresh eyes.
I rewatch my discs of that about once a year, and I love most of it. I think everyone in university either knew (or was) a (p)Rick, so that characterization is eternal. And every one of the musical numbers still sounds fantastic. I’ve tried to get through Bottom twice but it’s an uphill struggle.
I think the Marx Brothers hold up well, especially their Paramount movies and their first two MGM films. Room Service is quite funny, though not really the Marx Brothers and there are some great bits in A Night in Casablanca.
I’m a big fan for Chaplin and Keaton.
It’s a Gift with Fields (“Do you know a man named Carl LaFong? LaFong. Capital L, small a, capital F, small o, small n. small g. Carl LaFong.”
The Court Jester (“The pellet with the poison’s in the flagon with the dragon. The vessel with the pestle holds the brew that is true.”)
Young Frankenstein
Love and Death
Dr. Strangelove
Airplane
Mine is: “Oh, good. For a moment there I thought we were in trouble.”
Mel Brooks’ best movie (and the one that has held up the best) is still his first: The Producers.
The high school senior I interviewed for admission to my university’s Honors College yesterday said it was his favorite book, FWIW.
Good suggestion. The magnetic armor bit puts my kids on the floor.
I’ll grant you that one is a very strong competitor and it’d be coin toss as to which is better!
Also from a more recent movie:
“The greatest trick the devil ever pulled was convincing the world he didn’t exist”
The Usual Suspects
Just thought of one more, and very old:
“No, it wasn’t the airplanes. It was beauty that killed the beast”. King Kong
I think the consensus today is the portrayal of Jodi was overall not bad but it certainly had its flaws. In the grand scheme of things, the portrayal of Jodi was outrageous in a soap opera kind of way and in line with the rest of the show, but when you have so few gay characters represented on television, I can understand why people would be more sensitive to such portrayals. Jodi was presented in nothing but a sympathetic light when the mother of his child tried to cut him out of her life. That’s kind of a big deal in early 80s television.
This bit, in which Jodie (Crystal) is talking with his very sheltered, somewhat dippy aunt Jessica (Katherine Helmond) about homosexuality, still makes me laugh out loud.
I Love Lucy (well, it’s funny to me, anyway). Also, it was a game changer for TV: Lucy’s pregnancy, Ricky’s ethnicity (it always made me wonder why Lucy never seemed to learn Spanish, but maybe it made the comedy better that she didn’t), plus a housewife who wanted more in her life, her pleas to be in show business, etc.
Books:
Auntie Mame - 1955
The Milagro Beanfield War - 1974
TV:
Newhart
WKRP
Taxi
More recent TV
Frasier
The Larry Sanders Show
Seinfeld (although I’ve seen the eps so many times, it kinda drags now)
Movies:
The Russians Are Coming
Young Frankenstein - a perfect parody of old filmmaking
Harvey - 1950
Born Yesterday - 1950, with a hilarious turn by Judy Holliday, who played the role on Broadway and won an Oscar for the film version
My favorite final lines are from In Bruges.
There’s a Christmas tree somewhere in London with a bunch of presents underneath it that’ll never be opened. And I thought, if I survive all of this, I’d go to that house, apologize to the mother there, and accept whatever punishment she chose for me. Prison… death… didn’t matter. Because at least in prison and at least in death, you know, I wouldn’t be in fuckin’ Bruges. But then, like a flash, it came to me. And I realized, fuck man, maybe that’s what hell is: the entire rest of eternity spent in fuckin’ Bruges. And I really really hoped I wouldn’t die. I really really hoped I wouldn’t die.
*The Russians Are Coming, the Russians Are Coming" and the book it was based on, The Off-Islanders.
Soap, definitely.
A roommate had an omnibus volume of the first three books plus a foreword that talked about the history of the books/radio shows/&c. I found the foreword fascinating, but couldn’t get interested in the books at all.