If the problem is with local weather or air traffic control, all flights will probably be late and there is not much you or the airline can do to speed up your departure. If there is a mechanical problem with the plane for your particular flight or if the crew is delayed on an incoming flight, you might be better off trying to arrange another flight, as long as you do not have to pay a penalty or higher fare for changing your reservations. (It is sometimes easier to make such arrangements from a pay phone or cell phone than at a ticket counter.)
If you find a flight on another airline, ask the first airline to endorse your ticket to the new carrier, which could save you a fare increase. Remember, however, that there is no rule requiring an airline to do this. If you are using an electronic ticket, you will probably have to get paper documentation issued before it can be endorsed to another carrier.
If your flight is canceled, most airlines will rebook you on their next flight to your destination on which space is available, at no additional charge. If this involves a significant delay, find out if another carrier has seats and ask the first airline to endorse...