I take a travel bike along everywhere; it's an S&S coupled full size road bike. The typical checked baggage size and weight limits are 62" (height + width + depth) and 50 lbs (20kg some places internationally). I have a dedicated carry case that is 26"x26"x10" which meets that limit. They regularly bash the hell out of it, including breaking one of the latches last trip, but the bike usually comes through OK, and I just have to pay any regular checked baggage cost.
Pretty much all of the airlines will allow the bike on, often even unboxed as long as the handlebars are turned sideways and the pedals removed. This will be a trigger to get charged the bike fee, however, which can be as much as $300 one way internationally.