The major airlines
Sometimes you try all the tricks in the book yet still find the best airfares by going right to the horse's mouth: the Web sites of the major North American and European airlines
Major US and Canadian Airlines
Major European Airlines
Austrian Airlines (Austria; www.aua.com)
SN Brussels Airlines (Belgium; www.flysn.com)
Croatia Airlines (Croatia; www.croatiaairlines.hr)
CSA Czech Airlines (Czech Republic; www.czechairlines.com)
Finnair (Finland; www.finnair.com)
Air France (France; www.airfrance.com)
Lufthansa (Germany ; www.lufthansa.com)
Olympic Airways (Greece; www.olympicairlines.com)
IcelandAir (Iceland; www.icelandair.com)
Aer Lingus (Ireland; www.aerlingus.com)
Alitalia (Italy; www.alitalia.com)
KLM Royal Dutch Airlines (The Netherlands; www.klm.nl)
LOT Polish Airlines (Poland; www.lot.com)
TAP Air Portugal (Portugal; www.flytap.com)
SAS Scandinavian Airlines (Scandinavia; www.scandinavian.net)
Iberia (Spain; www.iberia.com)
Swiss (Switzerland; www.swiss.com)
Turkish Airlines (Turkey; www.turkishairlines.com)
Virgin Atlantic Airways (The UK; www.virginatlantic.com)
British Airways (The UK; www.ba.com)
Change amongst the current crop of major transatlantic carriers is not unlikely these days as the world's major airlines struggle for their very survival.
Witness in the U.S. all the recent airline mergers, the death of TWA, the dance in and out of bankruptcy being done by US Airways, United, Delta, Ameircan, and Air Canada—and the fact that the few biggies that are left spent much of the first decade of the new millennium begging Congress for billions in bailout dollars.
Europe is feeling it, too. Hungary's Malev airline was suddenly liquidated in 2012 (no doubt to the delight of Wizz Air, a low-cost carrier based in Budapest). Belgium's Sabena went belly-up in 2001 (replaced by SN Brussels, a rebranded regional charter run by Delta), and Swissair declared bankruptcy, surgically removed the legroom from their planes, and are now attempting to resuscitate their business under the rather uninventive new name "Swiss." Largely, they are failing, and are currently in talks with Lufthansa about a possible merger.
Not to be left out, Air France and KLM merged in 2003, which led Italy's Alitalia to start hopping up and down on the sidelines, waving its wings to try and convince the two to make it a threesome. (Alitalia eventually went bankrupt in 2008, but was bought out by an Italian consortium, reorginized, and continued to fly as usual.)
On the other hand, Aer Lingus has remodeled itself after Europe's no-frills airlines (we'll get to those on another page), with cheap intercontinental flights and transatlantic fares that frequently dip to just $99 each way.
In fact, for the cheapest transatlantic fares overall, look first to Aer Lingus, Iceland Air, Virgin Atlantic, and (because they have to compete with Virgin) British Airways.