You may have noticed that with tornadoes in the area, O'Hare was a bit of a mess yesterday. While airlines are doing their best to rebook passengers on different flights, the backlog has left some passengers stranded for days, subsisting on expensive airport food and stuck paying for unanticipated hotel stays. In some cases, passengers have given up entirely, instead renting a car and driving to their final destinations.
If you were among the unlucky air passengers to be stranded by the storm, what kind of compensation are you entitled to? It all depends on which airline you're booked on and the formal reason for your flight's cancellation or delay.
It depends. In general, you can get some kind of compensation if the airline is at fault, like if they oversold the flight and you were bumped, or if there's a mechanical issue. But if the cancellation was due to weather or other circumstances beyond the airlines' control, no compensation is required. Technically, that means that airlines don't owe anything to passengers who were left stranded by the weather.
However, just because they don't have to doesn't mean that they won't. JetBlue offered some compensation in the form of air miles when the Polar Vortex grounded flights in early 2014. Other airlines might offer similar compensation for weather-related delays, but probably will not offer it unless you ask directly. And the bottom line is that you SHOULD ask - especially if you paid for a hotel room or meals out of your own pocket.
The US Department of Transportation's page for airline consumers states that you can't be kept on the plane for more than 3 hours for a domestic flight, or 4 hours for international, without allowing passengers a chance to get off. There are safety and security exceptions, however, so if you were stuck on a plane for longer than is usually allowed during the storm, the airlines may cite safety concerns. Airlines fined for tarmac delays in the past have issued refunds, vouchers and frequent flyer miles for compensation, but it's the DOT that determines the amount of the fine for each individual incident, so there's no set amount or method.
If you are able to find a flight out with different airline, the DOT says that you should ask the first airline to "endorse" your new ticket to the new airline, which may prevent you from paying a fare increase above what you paid the first airline. Not all airlines do this, nor do they all honor such endorsements, but the worst that can happen is that they say no.
If your flight delay or cancellation leads you to cancel your whole trip, the airlines are required to refund any unused portion of your transportation. That includes non-refundable tickets and bag fees.
At the very least, you'll want to get to wherever you're going as quickly as possible, and there are some steps you can take to maximize your chances for a speedy rebooking.