From the USA
Delta Airlines Delta is a member of the Skyteam Alliance so you can access Air France and KLM airlines as well as many others.
American Airlines American is a member of OneWorld Alliance so you can get access to Iberia airlines as well as British Airways.
United Airlines United is a member of StarAlliance So you can also access Lufthansa among others.
Iberia Airlines Iberia is the national airlines or Spain.
British Airways British Airways is the national airline of Great Britten.
Aer Lingus Aer Lingus is the national airline of Ireland
Travel within Europe
Ryanair Ryanair has very cheap fares throughout Europe.
EasyJet Another airline with great discount fares
Flybe Various Spanish, French and Portuguese destinations.
Vueling A low-cost Spanish airline
Hop For internal flights in France. Great from Orly in Paris to Biarritz
Air Europa Flights from London to Madrid, internal flights in Spain.