Tire choices - UPDATED!

The DeLorean came from the factory fitted with Goodyear NCT radial tires in the following sizes:
Front - 195/60R14                       Rear - 235/60R15
Yes, the rears are 1" larger diameter than the fronts. The idea was that the larger tire would compensate for the uneven weight distribution of the car.
The Goodyear NCTs have been discontinued for many years. As new cars have moved on to larger tire sizes, it has made locating quality, performance tires for the DeLorean more difficult. It is not unusual to find cars still wearing the NCTs. They range from just hard and slippery to oval shaped and lumpy. In any case they are not safe for more than a drive around the parking lot, if they hold air at all.  
We drive many DeLoreans here in the course of road testing cars prior to delivery. Many of them come here with new tires, old tires, mis-matched tires, no name tires - you name it. So we have a lot of experience with different brands of tires that most DeLorean owners don't get in the course of their ownership.
Currently there is only one brand of tire available in the two original sizes in a matched set of four, the Hankook Kinergy ST SL.  
Another option is to go one size smaller in the rear only, to 225/60R15. This opens up some choices. As of August 2016 the following are available in the combination of 195/60R14 fronts and 225/60R15 rears:
Toyo Extensa
Vredestein Giugiaro
Ohtsu (formerly Falken) FP0612
Kuhmo Solus KR 21 (may be discontinued but locally available)
There may be other brands available in these sizes but we either have not tried them or do not recommend them. Due to constant changes in the market, please contact your DeLorean Motor Company location to see what they are currently installing on Customer Service vehicles. 
Some of the more popular replacements in the past have included the Yokohama AVS and Michelin Pilot tires - both of which have long been discontinued, so you need to pay attention to the age of the tire. Some automobile manufacturers recommend that consumers replace tires after 6 years from their production date while some tire manufacturers say a tire can last up to ten years with annual tire inspections and proper (indoor) storage.
We recommend that any tire - regardless of tread depth - be replaced after it is seven years old. Establishing the age of a tire can be tricky, especially on an older car.
Tires made after the year 2000 have a four digit code molded into the sidewall of the tire. The first two numbers are the week in which the tire was manufactured, and the second two numbers represent the year. Therefore, a tire with a date code of 3114, like shown below, was made in the 31st week of the year 2014.
Tires made before 2000 have a three digit code and are harder to decode. The first two numbers still represent the week of the year in which the tire was made, but the last single digit only tells you the year of the decade in which it was made. So a code of 519 can be the 51st week of 1999, 1989 or 1979. 
The original spare is a Goodyear Convenience Tire, commonly called "space-saver" or "mini-spare". This tire will fit either the front or back locations. It is normally suitable for short drives at low speed, just to get to the next tire store. The original tires, now at 35+ years old, are typically hard and don't hold air very well. They will generally fail if actually installed on the car.  
Replacements are available but may take a few calls to tire stores as most do not commonly carry them as a loose tire. The size you are looking for is T125/70D15. At the time of this writing, we have seen both Kuhmo and Bridgestone tires in this size. 
Written by James Espey, DeLorean Motor Company (Texas)
Revised 8/14/2016 DAS minor edits, brand updates.
Revised 9/13/2016 DAS added spare tire info