One thing that must be said here is that everyone is assuming that we are talking about radial tires.
Radial tires are about all that is available now because they are superior to bias ply in many areas.
However, radial tires can only be repaired if the puncture is in the tread area.
If the puncture is in the corner of the tire, that is in the transition area between the tread and sidewall, then this repair is questionable. I have tried to patch/plug a corner puncture but never been successful.
If puncture is in the sidewall of a radial tire, no reputable dealer will try to repair this area. This is one of the few shortcomings of radial tires.
The only other shortcoming that I know of radial tires is that when pushing them to the limit, they dont make alot of noise (squell-sp) and warn the driver like the old bias/ply tires. They just break away without any noise warning.
Other than that, radial tires are the greatest invention since bottled beer.
Ex-tire engineer
(who loves Michelin donuts...)