Fiats of any description.Including the Spyders.
I owned a Fiat for several years in the mid-1990s.
Of course, I was living in Italy at the time.
The Chevrolet Celebrity, especially the station wagon. When I owned one, it seemed like every third car on the road was one. Not long after it was diagnosed as terminal and was replaced, it became something of a phenomenon to even see one on the road. I think they all had congenital engine crappiness.
The Dodge Aspen was popular for awhile, and if we go farther back, the Buick Special, a nice little almost-compact.
ETA: Pontiac Tempest – I loved those.
Heck, even as recently 1999-2000, the Pontiac Grand Am
It’s like everybody at once decided to buy these cars. Don’t much see them on the road that much anymore.
Nearly all the small- or mid-sized Chevy sedans after the original, rear-wheel drive Nova have been apallingly chintzy, utterly disposable cars, and I say that even though I willingly paid cash money for a brand-new '78 Malibu wagon. What a fool I was. Meanwhile, my parents owned, in succession, a Vega, Chevette and Citation, and the memories of those dreary little light reconnaisance vehicles (the first two in yellow, yet) still give me nightmares decades later.
The Chevy Corsica and Beretta: exercises in constructing car-like devices from paper and foil. There were still a bunch around a couple of years ago, but they now seem to have mercifully disappeared. I have little doubt that about ten years from now, we’ll be saying the same thing about the current Malibu, not to mention the Cobalt sedan, which makes a mid-60’s Fiat look like a model of robust construction by contrast.
Just to show I’m not anti-American, I’ll throw in any first- or second-series Honda Civic or Accord. The oldest of either type one ever sees any more are early-90’s models, despite the marques’ general reputation for longetivity.
Add Mazda Miatas to the list. I don’t see them very often any more.
You’re not looking very hard. They are all over the Seattle area. Come to LA and you can’t swing a dead cat without hitting a Miata.
I was going to come in here and add Chevy Celebrity, but I see it’s already been mentioned.
So I’ll mention the Oldsmobile Cutlass and the Pontiac Fiero. And the Chevy Astro.
The Ford Cortina, Ford Escort, and Ford Laser used to be everywhere, but I haven’t seen many at all in recent years.
Minis (the original ones) were also very common when I was in High School, but appear to have all but vanished now.
Funny. I see one one every day. 
Starts and runs the first turn of the key.
I see most of the others (except the elusive Mustang II) on this list too, because I like hanging around junkyards.
Same thing went for the 2002 Chevy Cavalier, specifically black ones. I can think of at least two or three times where I almost got into someone elses in a crowded parking lot.
Ditto for the 80’s versions of Toyotas (I drove an econobox Tercel back then). Now once in a great while I’ll see a good old fashioned “Datsun” somewhere (they changed their name to Nissan in 1983).
It’s still not uncommon to see a Datsun 120Y or 180B on the roads here- they’re the stereotypical “Impoverished Uni Student” car. For some inexplicable reason, almost every 120Y or 180B ever sold in Australia and NZ appears to have been Orange or Dirty White. Occaisonally you see Red or Green ones, but they’re not as common.
Datsun ‘Z’ cars are almost completely extinct now (other than the new 350Z). They all rusted out.
I’ve noticed that the ranks of Camaros are rapidly thinning out. There are still plenty around, but they’d be my next candidate for ‘car that was once ubiquitous but suddenly vanished’.
Really, the same can be said for any popular car that stopped production more than 8-10 years ago. That’'s the average lifespan of new cars of 8-10 years ago. As they hit their service life, they start to become wrecker-bait at a rapdily increasing rate until they’re all gone.
Was that the minivan that was shaped alost exactly like a Federation shuttlecraft? Yeah, I miss those. I kept wanting to see one someone had painted to look like the Galileo II.
Mr.Moto,touche. The OP regards cars,but I think Iveco trucks are made by Fiat.
Catfish,which model?
I think the observation 9about rusty japanese cars0 is true; here in the NE, you never see older japanese cars-reason is, they rust-and once the rust spreads to the shock absorber towers, the frame basically collapses-there is no way to repair these cars. Now, in california, things are different-I saw a gorgeous 1976 ALFA Spider veloce-in tiptop condition! Such a car would have vanished from the roads here long ago.
I was going to post the Miata but didn’t for some reason. Haven’t seen one in years around here.
Okay, I lied, a co-worker drove one about a year ago. But I haven’t seen one in years on the road!
Strangely, I still see a lot of late 1980s and early 1990s Oldsmobile Cutlasses, Cieras and Cutlass Cieras around these parts. Same thing in western New York, too. I don’t see the Chevrolet Celebrity anymore, though, even though it’s built on the same platform.
There’s still plenty of Oldsmobiles on the roads around here in the Cleveland area, but what I don’t see anymore is the Aurora. Odd, because it was their highest end model.
I’ll also nominate GM F-body Camaros, Firebirds and Trans Ams as the next car to go “poof!”. A close cousin, third and fourth generation Chevrolet Monte Carlos that were the “guido car” of the 1980s, went poof! sometime in the late 1990s.