Keep in mind that because several airlines are no longer willing to pay commissions on tickets sold by online travel agencies, these agencies may either add a $10 surcharge to your bill if you book on that carrier--or neglect to offer those carriers' schedules.
The list of sites below is selective, not comprehensive. Some sites will have evolved or may have disappeared by the time you read this.
Travelocity (www.travelocity.com) and Expedia (www.expedia.com) are among the most popular sites, each offering an excellent range of options. Travelers search by destination, dates and cost.
Orbitz (www.orbitz.com) is a popular site launched by United, Delta, Northwest, American, and Continental airlines.
Priceline (www.priceline.com) lets you "name your price" for airline tickets, hotel rooms, and rental cars. For airline tickets, you can't say what time you want to fly--you have to accept any flight between 6am and 10pm on the dates you've selected, and you may have to make one or more stopovers. Tickets are nonrefundable, and no frequent-flyer miles are awarded.