We've flown many places over the last 10 years or so, always using the CTC poly bag method. Airlines include BA (Heathrow - Delhi), South African (Heathrow - Jo'burg - Cape Town), Emirates (BHX - Dubai - Cochin), Easyjet (Gatwick - Marrakech & Palermo), Thomson (BHX - Pula & Dubrovnik), Monarch (BHX - Gran Canaria, Tenerife, Malaga, Nice, Paphos, Larnaca), Norwegian (Gatwick - Bergen & Oslo, Oslo - Bodo & Alta - Oslo). Probably a few more that escape me too.
Disassembly is just front wheel out and strapped to frame, handlebars turned sideways, pedals off, rear derailleur removed and zip tied to chainstay with some bubble wrap round it. usually some padding or bubble wrap round the main tubes to protect from scratches. Rear wheel stays in, mudguards and rack stay on. Bike goes in poly bag with empty bottles in cages, and pedals + tools in saddle pack. Liberal amounts of duct tape to secure everything. Never had a problem, either with check in staff or baggage handlers and I think the most damage we've ever sustained is a broken mudguard. But then we're riding solid touring machines which will shrug off a bit of careless handling - I certainly wouldn't take this approach with an expensive soot bike.
We're usually touring independently, and very often point to point, so anything that requires left luggage/storage isn;t usually an option as we won't be returning to our arrival airport. The poly bags roll up to about the size of a water bottle and get bungee'd to the rear rack. We've got a couple of lightweight packable holdalls which take the panniers to minimise the number of bags to check in (only one usually needed unless we're camping). Handlebar bags and helmets get taken as hand luggage.
When it comes to airlines, for long haul Middle East & Asian carriers are much easier - standard baggage allowance is generally 30kg with no limit on number of bags and sporting equipment just goes in the normal baggage with no need to pay anything extra. European carriers are more varied ime. Short haul Monarch and Easyjet are our preferred airlines (mostly Monarch as they have a good selection of routes from our local airport BHX) - easy to book bikes online, and £30 is reasonable to me (Eurostar charge that to get a bike to Paris and they can;t even tell you when it'll arrive). I try to avoid Ruinair on principle, even without them charging £60.
Our last trip was back from Nice, with the tandem. A bit more disassembly, mostly to reduce the length but neither check in or the staff at outsize baggage batted an eyelid.