The biggest passenger airlines I thought are currently the ones generally in America: American Airlines, United Airlines, British Airways, Delta Air Lines, and Continental Airlines. There are many gigantic airlines out there, but focus in on the United States and western Europe, and in East Asia as well. These tend to be the general trends of where the mega-carriers are located. The three biggest I believe are American Airlines, British Airways, and United Airlines, and I suspect Delta and Continental aren't far behind.
Fly one thing; Fly it well