I had an employee with 275,000 on a Corvette C5. Nothing more than a water pump replacement. Ran like a scalded dog. The driver’s seat was crushed - but he replaced that with a boneyard seat.
At 300,000 he installed a 30K mile used transmission because the original was shifting a little funky. It is still running now at 450,000 miles or so. Still on the original engine.
personally:
My 2000 GMC Sierra. 190,000. Very little non-routine maintenance needed. I put a rad in it about 6 years ago, that I thought was a bit premature, but that is about it.
fleet wise (as I am a fleet mechanic):
I have seen several Ford 7.3L IDI Diesel engines (built by International,) go over 300,000 without even breaking a sweat. The Ford E4OD Trans would only go about 100,000, but those engines were solid as could be. We would have to scrap the vans because the bodies were falling apart, but nothing wrong with those engines.
I have a 1999 Ford Ranger at work with 240,000 on the engine. again, the trans conked out at 200,000, but engine is still going strong.
Maintaining fleets has left me wondering which of several vehicles was the most reliable. The Ford Econoline vans with the 300ci I-6 and the C-6 transmissions were so reliable that any failure before 300,000 miles was considered a DUD. And Toyota Hilux pickups were notorious for running until the fenders fell off with only relatively minor repairs well beyond 300,000 miles. All the GM H bodies of the 90s were capable of 300,000+ miles of reliable service but usually the first driver would reluctantly trade his car in after 200,000 miles because the interior was getting worn and the paint was fading. The there were the Cherokees. Those 1990 through the early 2000s with the I-6 engines were virtually bullet proof mechanically and fading paint was their most common failure. I have owned each of those models over the years, several I bought from fleets that I serviced. There are so many great models that others had more experience with than me, Crown Victorias for instance, that I would think it would be impossible to determine a MOST RELIABLE vehicle. And current Corollas may equal or surpass the great service of those “classics” that I mentioned.
I know, 100k miles used to seem like a lot of miles. Now I expect at least 200k miles out of a car.
I had a 1977 Lincoln Mark V that went 274K on the original engine and transmission. My father purchased it new and it became my daily driver 7 years later through mid college and beyond as I drove it for a couple of decades. A knock in the motor that was getting progressively worse convinced me to finally give it up.
Similar to the 7.3, the older Cummins engines generally lasted very well. There’s one at work with over 700k miles in a maintenance guy’s 1 ton Dodge. I think the transmission has given some issues, 6 speed manual. The maintenance guy who had it before the latest driver ran some sort of tuner on it. It had close to 700k miles with a tuner and ran great. I drove it home one night. Tons of torque, but the clutch would slip (I guess). If I gave it too much throttle in too high a gear at low rpm, it would start to “free rev”. I assume that was the clutch begging for mercy.
Curious if the newest diesels will be as reliable.
1998 Buick Regal LS, 165,000 before it was wrecked. Engine and transmission still fine.
2005 Honda Accord EX V6 w/ auto trans, 186,000 miles. When I traded it in, the used car manager remarked how peppy it was and how welll the trans shifted. Honda dealer, BTW.
Your dad’s car was likely a Toyota CORONA, not a Corolla which came in the 70s. The Corona was the first small car other than the VW Beetle that could be driven at freeway speeds all day with burning out its engine. It put French, Italian and British small cars to shame.
From then on, together with the Toyota Crown, Japanese cars set the standard for low cost imports. California was the first state to endorse these vehicles while they were still being made fun of in Texas, the Rust Belt and other conservative “Buy American” and Detroit Iron states.
Germans derided Japanese cars till the late 70s.
Korean cars went trough the same cycle, but their initial offerings had dismal quality although the price was right. My brother’s girlfriend had a 1986 Hyundai Pony, a pathetic car, except for the engine which was a Mitsubishi unit.
Best car I have owned was a 1981 Toyota Starlet. EPA rated at 50 mpg. Deepest I ever went into the engine in 275k miles was valve adjustment (twice). Looked and ran perfect when I sold it. I did have to replace the bearings in the 5 speed manual transmission, but that was my fault for putting the wrong weight oil in the transmission.
Second best car is a 1997 BMW 328i. 335k miles and still running strong and looking beautiful. Deepest I have gone into the engine was to remove the valve cover to replace the VANOS seals that had gotten old and hard after 18 years of use. Never touched the manual transmission other than shifter bushings. Replaced the (non-rebuildable) drive shaft once and rear wheel bearings twice.
Had to replace the dual mass flywheel when I installed its third clutch.
Nope! Corolla. But I had the year wrong. You got me curious so I called mom - it was a '70. Dunno why I’ve thought it was a '68 all these years. Mom tells me its name was Ralph. I’m glad naming cars isn’t a thing anymore. 
I still drive my cars that have been very reliable. But first, let me get my unreliable cars out of the way: 1978 Camaro Z28, 1990 Isuzu Trooper (that’s when GM got involved and everything GM was total garbage (engine, transmission, electronics…a nightmare on 4 wheels, mi inherited mid-‘90’s Buick Regal (worse than the Isuzu ad everything self-destructed), and my brother-in-laws early 2000’s Ram puckup (pile-I-crap with a Dodge emblem).
I still drive and love my 2002 Acura CL-S, my wife’s 2007 Acura RDX, and my love…a1999 4Runner 4WD. We bought my son’s Lexus IS350 which has been stellar and we plan on keeping that well past 200K miles.
2002 Saturn SL. Sold it in 2015 at 275k, still on the road.
DFilice - If we are going to compare notes on the least reliable cars, I once owned a 1972 Chevy Vega. Checkmate.
But they did have one of the weirdest methods of transport from the factory…
Well gee, if we’re talking worst cars, my 1960 Morris Minor beats them all. I don’t think I ever got more than 200 miles on it, and half of that was pushing it to start. Whaddaya expect for $125?
I attended a car show recently and there was a Morris Minor that had been in the family since new . All original and looked really good.
98 Corolla – 352K miles. Dated my wife with this car, married with this car, took 2 of my 4 baby girls home in this car, now my 15 year oldest daughter DRIVES this car. Normal maintenance. Only issue was when I was broad-sided in the rear corner, now it has a salvage title and still runs well. Still gets 30+ MPG in mixed driving. Interior just starting to fall apart with a falling headliner 
I had a Morris Minor as a company car when I had a summer job with a gas utility in 1959. As a gas inspector on new construction I had to visit the head office, 70 miles down the freeway, once a week. I was given a new vehicle and by the end of the summer had burned out nearly all the valves. The little cars just did nto stand up to fast highway driving, but that leather upholstery sure smelled good!
My most reliable vehicle was; believe it , or not, a 1983 Dodge Omni. I have no clue how many miles was on the OD when I sold it, but it ran flawlessly for 7 years. Bought new. Regular maintenance did the trick. The manual tranny, and clutch failed @ the same time, so I got rid of it. Dare I add, the local auto mechanics were a nightmare; from the car dealer to local garages, I couldn’t trust any of them. It took over a month for one to tell me the tranny was failing, even after I let them all drive it first. I liked the car, but didn’t want to invest a few hundred, or thousands into it at the time.
Out of the frying pan into the fire, my next car was a non-turbo SAAB, ugh!
I think the most reliable vehicle in our family is the 2006 Chevrolet Uplander I bought in 3006. It was a program vehicle with 15,000 on the odometer. My son now has the Uplander and it has gone over 200,000 miles without a major repair. It has the original fuel pump, alternator, water pump, etc.
Now I am not sure how one defines a major repair. The 2011 Toyota Sienna had to have a water pump at 90,000 miles. The cost, because of the labor involved, was $975. Does this count as a major repair?
The cost of ownership for the Uplander over the 100,000 miles I owned it over the cost of ownership of the Sienna over its first 100,000 miles was much less for the Uplander. Now I am not saying that the Sienna is an unreliable vehicle. In fact, I replaced the 2011 Sienna with a 2017 Sienna. When I think about the fact that I paid $16,000 for the Uplander as a program vehicle where the Sienna cost me $28,000, the Uplander was a much better buy.