Would a major electromagnetic pulse (EMP) leave most cars operable? According to C. Davis of the Ask a Prepper blog, after a major electromagnetic pulse:

Most electronics will be fried beyond repair and it will be years – in some cases decades – before anyone is able to start making replacements.

The blog specifically references motor vehicles.
On the other hand, Jason Torchinsky of Jalopnik claims that:

most cars would not be seriously affected

Is Torchinsky correct that if an EMP hit your city (say, from a nuclear blast), most cars would still be usable?
 A: Most cars will not be affected.
From the Report of the Commision to asses the thread to the United States from Electromagnetic pulse (EMP) attack

An EMP attack
  will certainly immediately disable a portion
  of the 130 million cars and 90 million
  trucks in operation in the United
  States
Approximately 10 percent of the vehicles on the road will stop, at
  least temporarily, thereby possibly triggering accidents, as well as
  congestion, at field levels above 25 kV/m

Page 115 of the report goes into more details but basically the vulnerability comes from the electronics in modern cars, however some of the effects are mitigated by improved electromagnetic interference practices/standards. 
Also if the car is not running at the time of the EMP, it will probably be OK. Of those that were running the effects were mostly minor, the most significant being engine stall but really no long term effects. 
The statement that an EMP will result in years of no automobiles is ludicrous. 
A: Hard to answer, since most of the information about HEMP is classified, but also because the question is too broad. Any kind of EMP is not going to affect the same a car in an underground parking than in the open, one right below the EMP source than one 2,000 miles away, one 1988 car or a 2015 car, and so on.
As a general rule, a HEMP caused by a nuclear explosion in the stratosphere can stop dead most modern cars in a large area (hundreds of miles). However, many of them can be restarted (if they don't crash as a result) or be repaired without too much hassle. You can google for articles about EMP effects on cars, such as this one but they all refer to the same report as a primary source: this study from the EMP commission, which is, to the best of my knowlegde, the only publicly available study ever made on EMP in cars.
The test was made using vintage cars from 1986 to 2005, and since they had to return the car after the tests, cars were tested starting with weak EMPs and were stopped whenever a car showed evidences of being affected. They concluded that most cars won't be affected by EMPs at all, or only suffer minor glitches (lights blinking, radio failing), but about 10% of cars could have their engines halting if surprised on the road, potentially causing accidents; however, newer cars with much more electronics and microchips may be way more vulnerable than the vintage cars that were tested.
