Airlines to use: KLM, Lufthansa, Air France.
My preference is KLM - punctual, competent, friendly, with good connections and good prices. I also like Amsterdam; it's easy and fast to go from Schiphol airport to Amsterdam Centraal station. I hate being stuck in some boring airport in the middle of nowhere. Lufthansa and Air France are efficient and work well, they just don't manage to give me quite the same feeling that I am welcome as KLM does, and Frankfurt and Paris aren't easily accessible from the airport.
I am sure that there are more airlines that fall into this category, but I have not used them, or not often enough to generalize here.
Airlines to avoid: British Airlines, Delta, TWA.
An unreliable, incompetent, and unfriendly airline can ruin your trip before it starts. British Airways, for example, is lucky if it predicts the departure day of its flights correctly. Expect to sit for the better part of the day in some cramped departure area because they can't rebook, can't let you leave (or they will remove your baggage "for security reasons", funny how the other airlines do it), can't give you any information, or, usually, can't be found. You need some enormous amount of business class mileage (the only kind that counts) before you get a card that entitles you to decent treatment, and until then you have to suffer their abuse. Flying Delta is similar, except that in addition to not knowing when you arrive you get the additional thrill of not knowing where you arrive, absolutely free. TWA does their best to compete, they consider their responsibility for you over when the plane touches the runway. These three airlines are on my blacklist because each delayed me for over 24 hours at least once and I got the feeling the problem is endemic.
The common denominator here is that employees may be friendly but have no clue what to do if something goes wrong, and consequently prefer to disappear when you need them most, and things go wrong frequently. Who cares if you stay half of the night in the airport, dodging cleaning crews in poorly lit halls, trying to figure out where the bus to the hotel leaves. Any airline can run into a problem, what counts is how the airline staff handles the problem and get you to your destination efficiently.
Generally, don't use U.S. airlines because they will want to shuttle you through their hubs, which frequently means missed connections. I had to stay overnight in airport hotels several times already. And, I do not warn about an airline here if a mistake happened once, only when it happens more often than not and I become convinced that it's a systematic problem.
General advice: Do not forget to ask the airline - not the travel agent - whether the flight uses aircraft large enough to hold a bicycle. Most airlines (not British Airways) accept advance seat reservations. Order a vegetarian meal if you fly economy because while the other passengers try to eat their rubber chickens or rancid lasagna you'll get (more or less) fresh fruit and vegetables. Don't do this in business class; the food there is ok and if you order vegetarian you may get economy fare! If you fly economy, bring earplugs and eye covers, and get a window seat so you can sleep. I always stay the night before a west-bound intercontinental flight awake to avoid jet lag. Exit rows are spacious, but do not get a window seat in an exit row of a widebody jet (Airbus 320, Boeing 747) because the emergency slide box will leave you almost no space for your legs. Several times already I had to repair the video screen of my (business class) seat because some connector shook loose, so bring tools and some spare wires or paper clips :-)
see also article on "shipping bicycle by train"
