Having appropriate luggage can make a world of difference. It may mean the difference between carry-on and stowed (which may mean the difference between lost and not lost!), health or a hurting back, and damaged vs. undamaged belongings.
Note: This article assumes that you are packing for a plane flight; travelling by train, bus, or car may be slightly different.
Garment bags can be exceptionally nice for short business trips. Most airplanes have little compartments with a bar that you can hang them on. Be advised, however, that those compartments fill up pretty quickly, and you may have to jam it into an overhead bin, wrinkling your suits and dresses.
However, garment bags are not particularly easy to carry if very full or for a great distance. (Note: I have never been a broad-shouldered, narrow-hipped, tall, strong man, so perhaps there is a class of people for whom this assertion is not true.)
If you must take heavy items (like, for example, six computer manuals and a replacement power supply), seriously consider some sort of wheeled contraption. One can purchase carts that can fold up and go inside the suitcase or suitcases that have wheels and a handle built in.
Suitcases with stiff, center-mounted racks are much more manageable than suitcases with "leashes". The leashed suitcases have a tendency to wobble, tip, get stuck, fall over, etc. The leash is always too short for your height, so you end up walking hunched over anyways. Leashed luggage is exceptionally ill-suited for those lovely, picturesque cobbled streets that your charming little pensione with no elevator is on.
A good, hard-sided suitcase with a rack can be a bit pricey. However, consider that this is much, much, MUCH cheaper than back surgery.
On the opposite end of the spectrum, you should remember that it is not mandatory to purchase a special valise for carry-on items. A few sturdy garbage bags can work just fine.
You can also put things in boxes. Be sure to wrap them extremely securely with glass-reinforced tape, and recognize that they will get very rough handling. Furthermore, the airlines will not take responsibility for damaging anything in a cardboard box. You take your chances.
For long-term, low-end travels (e.g. the Grand Eurail Tour of Europe), my personal luggage of choice is an old, beat up, blue nylon duffle bag. It is large enough to take a week's worth of clothes (if I am not too fussy) and small enough that I can't fill it fuller than I can easily carry. It fits in the overhead compartment and it weighs practically nothing.
Furthermore, it does not scream "Wealthy Tourist!!"; I could just be returning from figure-skating practice or something like that.
Backpacks and Camping Gear
You can ship camping-style backpacks as well. Some airlines will put them in large plastic bags to help keep things from tearing off. Otherwise, make sure that anything that you have attached to the pack (sleeping bag, tent, roll) is securely fastened. 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.
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. Some airports and/or airlines may have places to leave your luggage; it would be prudent to make arrangements well before you leave. 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. You can probably count on an airline at a major airport to be able to sell you bike boxes (US$10 at San Francisco International), but it may take them 30 minutes to find them. Smaller airports might not have them at all.
The bicycle boxes that the airlines provide are huge. This is good and bad; your bicycle will fit with minimum disassmbly, but all that extra room will allow your bike to slosh around. This is the most dangerous method of shipping your bike.
The best compromise is probably to go to a bicycle shop and get a bicycle box from them. This box will probably fit your bike better, but will require more creative disassembly. When you get the box, also ask them for a fork brace.
Article by Kaitlin Duck Sherwood, 1994