The real question is where the failure occurs. If it is in the early warning systems (the flock of birds, or a gas plume from an oil refinery, etc.), then there is a real chance of a mass launch. If that happens, we are all toast (albeit glowing toast), as it is unlikely that the damage/response could be contained at an acceptable level.
I am not sure how you can get a 'single' launch (i.e., some sort of failure in the chain of command), were one missile/bomber/etc. is used against the 'bad guys', since these systems all have PALs, and thus require some sort of authorization for use. Subs and missile silos both get orders to execute orders, as it were (Subs listen for messages at preset times, missile silos get the orders from their command centers), while bombers have their well-known 'fail-safe' points. Short of some sort of massive software screw-up (unlikely, given how many layers of checks and double-checks exist, and how procedures have been evolved to deal with this), I think that it is unlikely you would see this sort of failure event.
Now, rather than looking at the later part of our atomic age (say 1975 and later), what about the early period? Single launch failures, runaway bombers, rogue commanders, etc, would have been far, far more likely in the 50s and early 60s. Everything was slower (bombers took hours to get to their targets, missiles tended to be liquid-fueled, and thus took quite some time to launch, etc.), and the comm networks of the time weren't geared to rapid-fire response times, hence giving leaders some time to think about their actions...