As was seen recently with Hurricane Sandy (and the residual effects are still there), large portions of the East Coast of the US had major disruption to their air travel. There were also similar effects in Europe in 2011 due to the ash cloud from the volcano in Iceland.
For example, I had a flight booked this week from Pittsburgh to London, via Chicago. For several days Pittsburgh airport was closed and/or flights were (at least from my perspective) randomly cancelled due to aircraft being out-of-position, etc. Fortunately in the end I was lucky and my flight took off on time. Not everyone was so fortunate.
I know from past experience that when a flight is cancelled in these kind of circumstances (which often doesn't happen until less than 24 hours before, as the airline can't predict exactly what will happen), folks can get bumped onto flights several days later, as those are the first with spare seats.
What techniques exist, from the perspective of the traveller, for increasing the chances of getting to their destination promptly (either avoiding cancelled flights or getting a reschedule onto a flight shortly after)? Let's assume the traveller might be prepared to spend some additional money, but doesn't have the money for a private jet or a taxi cross-country.