I think one way to help with the "OMG PANIC!!!!!" mode that many people get into is to somehow, someway, practice for situations like stuck gas pedals, non-responsive brake pedals, driving off the road and over-correcting, skidding, etc etc etc.

I remember in our drivers ed class they TOLD us what to do in certain situations, but we never actually PRACTICED what they told us.
I was telling my dad this and before long he was trying to simulate certain situations with me behind the wheel. The first time I was driving his old truck and it started skidding (thanks to icy roads and no ABS) I freaked, but after doing it enough I'm much more confident with myself.
It's just my but if people were to actually practice for a situations like this they might subconsciously remember how to react correctly instead of going into "panic mode."