Nuclear power stations (are they building these anymore?)
- INTERFERON: this stuff was supposed to cure cancer, TB, a host of other illnesses, and put a shine on your mother’s silverware! Problem: it didn’t work! Not only that , but people taking it experienced severe side effects (including death). But it was touted to the skies…for a while!
- Catastrophe Theory: supposedly this was the mathematics discovey of the century. Only it had no applications that worked!
Or as a weapon/mind control device, for that matter.
The American SST. (Could have made the Concorde look like a pansy.)
War on Drugs 
I don’t think that war was officially declared until the Carter era. Before that time, we were just giving them something to fight over. 
Hey, it’s Robocop’s grandpa!
I have no first-hand experience with push-button transmissions, but when I’ve read about them, I always worried that they’d be easy to accidentally bump and shift into reverse or park when going 60.
Was this the case?
Or was the design good enough to protect against this?
If the former, I would reckon this is why they didn’t catch on.
Isn’t interferon still used, as part of the drug cocktail used to treat AIDS? Not a panacaea, to be sure, and like any drug, it needs to be used properly, but treating AIDS doesn’t sound like a failure to me.
In the cars I’ve seen, the push-buttons were always on the dashboard, well out of the way of the normal stuff (in my '62 Chrysler, it was at the top left of the instrument panel, right next to the door, and the only things near it were the knobs for the headlights and windshield wipers).
The only reason I suspect they died is because a lot of full size cars still came with three-on-the-tree manual transmissions, so the manufacturers would have to install different panels for those cars. In other words, not because customers didn’t like them, but because they were an added cost that customers didn’t care about one way or the other.
The idea that if you raise boys and girls exactly the same with no gender expectations they will come out exactly the same with no gender differences.
My mom and dad sure tried hard on this one, but I just played with my brothers’ dolls while they played with my trucks.
Which is not to say we should TRY to impose gender stereotypes on our children.
“Bubble gum” pop music.
The draft.
Psychedelic art (think: Peter Max).
Black lights in bars.
Nehru jackets (damn, I wish they’d come back).
Pop and op art
Thinking that the world as we knew it would come to an end if the Beatles broke up.
Thinking that it was Yoko’s fault when they did.
The Summer of Love.
Riots on college campuses.
Guys with long hair and full beards.
Folk music.
Ayn Rand fan clubs on college campuses.
Short dresses with an “empire” waist.
“Hip” variety shows.
Totally unprotected sex with no serious consequences.
The fear of getting arrested and/or beaten up if you were in a gay bar that got busted.
A secret signal in gay bars, telling people to “straighten up” because the Vice Squad was paying a visit.
Granny glasses.
Beads and peace-sign jewelry.
Clothing with flower patterns.
Girls with long, straight hair (even if they had to iron it).
“Light shows.”
Pea coats and long, thick scarves.
The quasi-military look (think: Sgt. Pepper)
“Oh, wow, man . . .”
Zidovudine (AZT, Retrovir) was developed in 1964 as an anti-cancer drug. It didn’t perform well, so it was shelved. In 1987, it became the first HIV/AIDS drug to be approved. Toxic stuff, but it was better than nothing.
It’s still used in combination meds (all-in-one pills rather than a bunch of pills); Combivir and Trizivir are two of them.
But it was developed in 1964, so I guess it doesn’t qualify for this thread. 
Maybe they should have televised it.
The Black Panthers.
I remember remarking on that to my dad in the late 80s, when one of the (probably all white) little-kid soccer teams in town voted to name itself “Black Panthers”. I don’t think any of the kids had heard of the group at all. I was a teenager, and I barely had. They just weren’t mentioned any more.
Er, a nitpick: the draft was around for long enough before the 60s that I don’t think you could call it an “experiment.”
How about the Yippies? 
and, it didn’t actually fail, they just stopped doing it.
Xray machines in shoe stores. (this mighta been late 50’s)