It fits in the overhead compartment and it weighs practically nothing. You can ship camping-style backpacks as well. Some airlines will put them in large plastic bags to help keep things from tearing off. And, as with packing in cardboard boxes, airlines will not take responsibility for damaging anything in a backpack. Do not pack the good china in the backpack.
Bicycles There exist hard-shell bicycle cases.
Shipping your bike in one of these is the least dangerous to your bicycle. Unfortunately, these cases do not strap onto bike racks particularly well, so you will have to find some place to leave the case while you are out touring the countryside. A good rule of thumb is that the more domestic terrorism there is, the less likely you will be able to find a good place to leave your luggage. You can also ship your bicycle in a cardboard box. Smaller airports might not have them at all.