I've tended to get my cars old...very old. Sometimes older than me! So while I've had some POS'es, I can't fully blame the manufacturer. But, for the worst car I've ever owned, I'd have to say it was a tie between a 1988 Chrysler LeBaron turbo coupe and a 1982 Cutlass Supreme coupe.
The Cutlass Supreme was only $800, purchased in 1993, with 61,000 miles on it. Transmission went out soon after, but was only around $675 to rebuild. The transmission shop said they could probably get it running more or less right for around $150, but that the problem would probably come back. I thought I'd keep that car forever, so I paid for a rebuild. It was fairly good after that for a little while. Needed new front brakes and tires, which are really just maintenance items. And valve cover gaskets, which were minor. But, around the 71 or so thousand mile mark, the 231 V-6 engine lost all oil pressure. A friend of mine replaced the gears in the pump, and got it to run again, but it wasn't long for this earth. I sold it, still running, with around 73,000 miles, for $400.
The Chrysler LeBaron was bought used by my uncle, for around $10,000, in 1990. He sold it to me when I got married, 5 years later, for $2,000. I think it had around 75,000 miles on it by that time. He'd had some work done on it, but nothing too major. It had occasional computer/electrical problems.
When we had it, it was also fairly reliable, up to around 90,000 miles. We had the timing belt replaced (should've been done at 60K, but we let it lapse), and it also needed a camshaft and crankshaft seal (no big deal), but it also needed some major suspension work.
When I got divorced, I let the ex wife have it. In that timeframe, the air conditioner compressor seized up, it needed a new radiator, burned up a couple of sensors, one that caused the engine to idle at 2000 rpm or so. Power antenna broke. Transmission started leaking. The turbocharger stopped working. The last straw was when it blew the head gasket around 118,000 miles or so. She took it someplace and had a new gasket and used head put on, but it still wasn't running right. I told her to let me borrow it and take it to my mechanic. He was able to get it to kinda run, for about $75...said a lot of the vacuum hoses and wires weren't hooked up right. But he also did a compression check on the engine, said it was shot, and to NOT put another dime into it!