My three favorite airlines are harder to determine these days, as they all seem to be competing for bottom spots. I used to like United allot, but they have been a disappointment for some time. When I was growing up in Atlanta, I thought Delta was the real airline, Eastern was second rate (turns out that was an understatement), and everyone else didn't even count. When I lived in Charlotte in the late '80's, Piedmont was great. Then it because USAir, then USAirways, then a struggling airline like many others.
In full disclosure, in addition to the above, and not counting the baby carriers (Delta Connection, etc.), I have flown American, Continental, Jet Blue, Midwest, Air Tran, ATA, Alaska Air, Southwest, Northwest, Air Canada, Aero Mexico, Mexicana, LOT, TAP Air Portugal, SAS, ANA, Qantas, Porter, Lufthansa, LuxAir, VRG, BMI, Aer Lingus, Virgin Airways, Air France, Swiss Air, British Airways, KLM, and I'm sure a few others I am forgetting right now. I have had elite status at some point on Piedmont, USAirways, United, American, and British Airways. This doesn't take into account defunct airlines like TWA, Eastern, Pan AM, etc.
Now for the top three.
Number three is American. They have generally clean planes, they tend to nickel dime you a bit less than United, and have good routes. They generally are competitive with their pricing. The flight crews, as you would expect with any large airline, are all over the map (no pun intended!). That said, they are generally better rather than worse, as are their gate agents. Their loyalty program is fair, and they seem to somewhat truly value their loyal travelers. I don't get terribly excited about American, but I don't feel the need to change either. They are my default airline for US domestic travel. That said, they may get international travel better than some (like United or USAirways), but there are others they don't match, such as BA or ANA or Qantas.
Number two is Porter Airlines. If you don't travel to Toronto from a Porter location, then there would really be no reason to know them. If you do, then there is no reason not to know them, or fly them. They have a unique deal going. They fly all new, roughly 80 person prop jets. They are smooth, clean, and comfortable, Their flight crews are better than most buy a long shot. But the killer is that they fly in to Billy Bishop ("Island") Airport instead of Pearson. Flying into Pearson is tedious, not to mention remote. Island Airport is located in the bay next to downtown Toronto. You literally take a ferry about 100 yards to get from the airport to the ground access point. I fly between Chicago and Toronto all the time, and it's great.
Number one, British Airways. I love BA. I have been a gold card holder for 10 years, and with all of their hierarchical recognition (royalty and all), that seems to mean more with them than elite status on many other airlines. They really get international travel. Really. The flight crews are almost always fantastic. Not always, but almost. The planes are generally outfitted better than most. Business Class ("Club World") sets the standard in my books for what business class should be. True 180 sleepers. Superb service. Excellent food. The arrival and departure lounges are the real deal. The lounges, especially the main lounge in Terminal 5 at Heathrow, are spectacular. And to make this personal, the ground staff in Chicago, my real window into BA, sets the standard for ANY travel industry participant, not just airlines. They are great, but the true embodiment of service is through two of their top people on the ground, Marcia Curtis and especially Judy Way. I love them both. When we sold my last company and I drastically slowed my trips between Chicago and London, I was probably more disappointed about not seeing Marcia and Judy more than most of the people I worked with. Judy is the best I have ever known. On the down side, BA tends to be more expensive. In my role with a small company, I have to be very, very judicious about where I draw the lines. I mostly fly coach (and I will take BA coach over others as well). When the price is within striking distance, I always opt for BA, believing that the extra money is justified by the better flight and the importance of that, once on the ground in terms of productivity. And yes, I really believe that. After millions of miles, some things start to sink in.
Honorable mentions go to Jet Blue, ANA, and Qantas.