Finding a bad car is pretty easy, we all pretty much remember what was pure unmitigated junk, or we didn't do our homework and bought something we regreted. Sometimes though, a decent car will get stuck with a really horrible engine... here's my nominee for this thread:

The Toyota 3VZE.

Usually when we think of Toyota trucks, we think of simple and sturdy compact trucks that last 500,000+ miles on their economical and sturdy 22R 4 cylinders. However in the late 80's, Nissan offered their Hardbody pickup with the VG30E V6, Ford had the 2.9 V6 and later 4.0 V6 in their Ranger and Chevrolet had the 2.8 V6 and later on the 4.3 V6. Toyota needed a V6 to compete with the other trucks. What they came out with was bad, really bad. The 3VZE was a 3.0 liter SOHC V6, the only non- DOHC V6 Toyota has sold, which makes it an oddball. However this motor became notorious for blowing head gaskets (repeatedly), which resulted in multiple recalls, plus the engine was underpowered, lord help you if it was automatic. Plus this engine boasted the fuel economy of a V8 engine, without the power or torque of said V8. Not that it mattered because plenty of these engines blew themselves to pieces and wise owners replaced it with Toyota's proven 22R series of engines. The 3VZE is more then likely Toyota's most hated engine, one that is best avoided. I know first hand because I sell Toyota parts!

Another example is sort of an interesting one, but this example shows what can happen when an engine isn't up to task for a car. Anybody remember the '79-'81 Dodge St. Regis? No? The St. Regis replaced the full sized Dodge Monaco, the St. Regis was smaller, but still very much a fullsize sedan. It had clear plexi-glass headight covers that retracted and could be had with the slant 6 or if you wanted more a 318 V8 or the 360 V8. Trouble was, nobody bought these, EXCEPT for fleet sales- specifically as police cars. With the 360, they made an acceptible patrol car, trouble was, not everyone could get it. In 1980, the only engine certified for use in the state of California in a Mopar police car was the 4 barrel 318 with all of 155 horsepower! Imagine being a Highway Patrol officer who just had a 440 Monaco that could do about 130 MPH (if there was no lightbar on the roof) and then went to the St. Regis as a replacement. 19 second quartermile time with a 95 MPH top speed. The problem was so bad and so many cops were miffed about the issue the CHP adopted the 5.0 Mustang GL as a pursuit car the next year and thus accentuated Dodge's fast fall frome grace.