There are two types of airfare: with restrictions, and unrestricted or full-fare.
Unrestricted/full-fare means you can make changes at will, or even get your money back. It gives you more flexibility with your travel plans, and thus many business travelers chose it for this very reason. But you pay through the nose for it when compared to the restricted fares on the same flight.
Restricted means just that. That's what most vacation travelers use. It's cheaper than full-fare (MUCH cheaper in many cases) but of course there are all sorts of strings attached, like non-refundable, non-transferable, advance purchase required, and the ubiquitous "any changes will result in a change fee + any additional airfare if any." The latter is because airfares generally get more expensive as the plane fills up (you actually see it in action on some airline websites such as Southwest), and also because airfares change often sometimes daily. In exchange for a cheaper airfare, you gamble that your travel plans won't change.
The only time the airline is obligated to put you on another flight without having to pay more is when it's either their fault (overbooking), or because of a covered delay such as caused by mechanical or weather conditions. With overbooking, if the airline cannot find a volunteer to give up a seat for you, you are actually entitled to a certain amount of compensation. For the others, the airline generally tries to get you on the next available flight(s) to your destination, with varying degrees of compensation as to food and overnight accomodations depending on the airline and maybe even the class of service you purchased.
Bruce is correct...when you purchase an airline ticket, you literally are purchasing something called a "Contract of Carriage." Most of us don't read it, but we should, as it's a binding contract. You signed it when you signed your name on the credit card receipt, and if you bought your ticket online, it's in the fine print of the last page (and sometimes requires you to check a box acknowledging it) before the "purchase" button appears.
That's why travel insurance is so important. I learned this lesson the hard way when my mother had to be scheduled for emergency surgery right before my Maui trip. I was able to reschedule the air travel part (with the change fee of course, fortunately the airfare remained the same for the new dates) but because I had purchased the rental car and hotel as part of a package, and did NOT buy the insurance at the time, I had to eat those costs
