I met a couple who go every year to the Yucatan in Mexico and use their folding bicycles that go be air and then are carried on the bus to the town they will use for their base. This would also be great for larger islands in places like Northwest USA and Canada and the Caribbean. Even Europe along the rivers and canals where I have use a rental bike a folding bike would have worked equally well. In Europe and China where there are high speed trains you can take the folding bike with you into a passenger car and put it in the special luggage section of the car. I greatly prefer dealing with motorists in Europe and Asia to those in the USA which are very aggressive on the whole.
Check though on luggage rates for the airlines as it varies widely and they give great rates for golf clups and surf boards and skiis but make up the differene with "irregular" luggage.