If you've been flying long enough, you've probably heard all the reasons that the airline can't get you to your destination on time. Weather is the cause you've probably heard the most, but we've all been on flights that were delayed for mechanical problems. Perhaps the most frustrating is the flight for which you have a reservation and a ticket but no seat and are told that the flight is oversold. In order to make correct decisions when these situations arise, you need to know what your choices are.
Weather: Because it is out of their control, the airline has no responsibility to you if the flight is delayed because of weather, other than to get the flight out when conditions and air traffic control will allow. Weather delays can occur because of the weather in your home city, at your destination, in between, or, really, just about anywhere. Your airline may allow you to change your ticket to an earlier or later flight (even for the following day) without a change fee if severe weather is expected to affect your flight schedule: the airline has no interest in having frustrated passengers stranded at the airport. Speak to the gate agent or call your travel agent for help in rebooking alternatives.
Mechanical: Each airline has its own "contract of carriage," which specifies its obligations to you when a flight is delayed or canceled for mechanical reasons; while similar, no airline rules are exactly the same. Most of the major airlines (excluding, in particular, Southwest and JetBlue) have "interline" agreements with other carriers. Their "contract of carriage" generally require that they put you on the next flight to your destination, whether on their airline or on another, when you are delayed in excess of a specified amount of time for mechanical reasons. Airlines will typically not offer to put you on another carrier's flight because that costs them money. When talking with a representative, ask when the next available flight is, if there is a flight to a nearby airport available or if they will endorse your ticket to another airline. If you are fortunate enough to get on another airline's flight, be aware that you'll have to check in with their ticket counter to receive the boarding pass and seat assignment.
Finally, if the flight delay ruins a scheduled trip, whether for weather or mechanical reasons, you are entitled to a full refund (even if you purchased a non-refundable ticket). You can ask for your refund at the gate or the ticket counter.