I've not flown with my bike now for almost 8 years. In the past most airlines would sell you a HUGE box at the baggage check in counter for $10-$15. I'd always use that, pay the oversize fee, throw it away at the destination and ceremoniously ride my loaded bike through the electric doors of the terminal. On the return I'd reverse the procedure and buy a new box. Back then Air Canada provided a huge plastic bag which worked fine. Now their website says a box is required. Most other airlines require a box.

Perhaps the $10 box is now history? Maybe that's the case with discount bike baggage airlines like SW? If available it's the easiest way to bring a bike with minimal disassembly. Pedals off and bars turned... you're good to go. Frame is reinforced by both wheels being installed rather than one removed packed to the side where it might get pressed into the frame. Plenty of extra room for fenders, racks and maybe even a tent strapped on. As stated above by gerryl, the simplicity of the plastic bag is equally good if permitted by your airline. Also makes it easy for the baggage handler as the bike can be carried by the top tube through the bag.

edit: At the start or finish of a trip I'll sometimes visit an airport to confirm the availability of a bike box or bag. It's usually impossible to make a direct phone call to a baggage counter.