I usualy go to ITA's web-site (beta.itasoftware.com) first. This is the booking engine that is used by Orbitz and will be used by Delta in the future... it checks out the adjacent airports, lays out the fares neatly among all the airlines.
Then I go to the airline I want to use for booking so as to get the online booking bonus.
Rarely, very rarely, does the ITA tool give me a different fare than the airline's site.
[This message has been edited by abigail (edited 03-18-2002).]