First and foremost, immediately call the airline's reservations office as soon as your flight is canceled, or a delay will cause you to miss a connection. If you're at the airport, do this as you join the line at the customer service desk. Since call centers typically employ hundreds of agents at a time, chances are you'll get through faster on the phone than waiting for one of the few agents at the desk.
If you're successful in getting re-booked on the phone, ask whether or not you need to see a live agent to get a new boarding pass before stepping out of the line. If you can use a kiosk or mobile app to check-in for your new flight, then and only then is it safe to get out of line.
Consider buying a day pass to the airline's lounge if you're not already a member. In my experience, the customer service lines inside the lounge are significantly shorter than what you'll find in the main terminal. Also, the agents working inside the lounge are typically more experienced and might be able to find new flights faster than their colleagues on the concourse.
In many cases, airlines will waive fees, refund non-refundable tickets and extend the validity of your ticket if disruptions are anticipated. And airlines are becoming increasingly proactive in issuing travel waivers as storms hit.
Most airlines, including American, Delta, United and US Airways, have issued waivers for the current storm. You'll save yourself a major headache if you check the airline's website before heading to the airport to see if you can change your plans from home.
Finally, if you do get stuck in an airport for hours, consider downloading helpful apps that detail airport amenities and transportation options. (Read more: From Food to Transportation Options, New App Targets Travelers)