Assuming that you won't be in one place long enough to have a postal address, you have three choices of places to collect mail:
What mail carrier to use, and where to have your mail sent, depends on what you need sent, how much you're willing to spend, and how much time you have. This problem really has to be broken up into five possible scenarios:
My first response is "don't bother." If you're only going to be gone a couple weeks, you probably won't be able to receive any mail, unless it's delivered to you by an express service (Federal Express, DHL, etc.), which is expensive. "Normal" letter and package services are far too slow and imprecise. That is, your letter could arrive in three days from the other side of the world, or it could take three weeks. Why bother with the hassle, if you're going home so soon?
If you absolutely MUST get a letter or package, have it sent by a registered, trackable, fast-as-possible ("overnight" service is generally not available overseas, you generally have to go "2nd day" or "priority" mail). If you're going to have it sent to a post office, make sure you have an exact address, and contact the office FIRST, to make sure they hold mail.
If you're staying in one place for an extended period of time, your best bet is to find a specific post office in the city where you'll be, make sure they hold mail, let them know you'll be receiving mail there, and ask them exactly how to have your mail addressed. NOTE: Having letters sent Care Of friends abroad is a fine idea, but many countries do NOT deliver packages (only letters) to residences, so if you have a package sent, your friend may have to go to the PO and pick them up, and there may be a fee! Check first!)
If you need a letter in a hurry, your best bet is to have it faxed. Many Post Offices have the ability to receive faxes, as do most travel service offices such as American Express. If you're receiving a package or a letter which can't be faxed (something that requires a signature, for example), then it's probably worth the money to go with a service like Federal Express. It costs around $20, but it's trackable (make sure you get the tracking number!), insurable and fast. I recommend having it sent to someplace you know the address of, such as a reputable hotel. It may even be worth your while to book a night at a slightly more upscale hotel if yours refuses to hold mail or doesn't seem trustworthy. In a true emergency, though, contact your nearest consulate or embassy for advice; I take absolutely NO responsibility for success or lack thereof.
If you're going to be gone for a long time, but know exactly where you're going to be in when, then you're in luck. You can use the cheapest forms of mail, and you won't have to worry about whether or not to stop someplace in order to collect your mail. The only thing I would particularly recommend AGAINST is sending any sort of package via "surface mail." Surface mail can take up to six months or more to arrive at its destination. This is what you use when you're sending stuff home, and you don't give a damn how long it takes to get home (or IF it gets home). Normal air mail of a letter or reasonably sized package should take no more than two weeks, but I'd give it three to be safe, especially if you live in (or are having mail sent to) Australia. So, give your friends and family your itinerary, the cities where you want to collect your mail, and the addresses where you're going to have it sent (your hotel, a post office or an office like American Express), and you're on your way. Make sure everybody leaves plenty of time between the time they send their mail and the time you expect to pick it up. (Note: "Mail forwarding" is a big advantage of sending letter to an American Express office)
Receiving mail (the tangible kind, not the electronic kind) can be a real pain in the rear while you're on the go. It's a bit like trying to hit a target moving in an unknown direction with a projectile of unknown velocity. If that sentence threw you for a loop, here's the problem broken down into its component problems:
Your best bet, therefore, is to either use a safe, reliable, fast, and unfortunately EXPENSIVE carrier, such as Federal Express, or to let your family and friends know of at least a couple places where you know for SURE that you're going to visit. (It's a good bet, for example, that if you're touring France, you're probably going to visit Paris.) Make sure you give them at least four weeks before you tell them where to send something, so that they don't have to run out to the post office that day in order to make sure it gets there in time. Of course, you're not on a fixed itinerary, so you can always wait around for something to arrive, but... I'm sure you don't want to do that.
If all else fails, and for some reason your package or letter doesn't arrive in time and you're just absolutely itchin' to leave, most places will eventually return mail which is never collected. It may be MONTHS before it's returned, but chances are that it will eventually head back home.
Most youth hostels and hotels will hold mail for you, particularly if they know in advance that it's coming, and if you already have a reservation. Call in advance and ask if they'll hold mail, and ask how to address it. Simple as that.
Almost every country in the world has a system of holding mail for people who do not have permanent postal addresses. In most countries, the system is called "Poste Restante." The way it works is that you send a letter to a post office, addressed to the intended recipient, and then the recipient has to go into the post office WITH HIS/HER PASSPORT (most post offices will not release mail without a passport or other suitable ID) and collect whatever is waiting. Many PO's have a special desk for Poste Restante, and many charge for the service (though usually only about $0.50/letter or so).
Generally, held mail should be addressed like so:
LASTNAME, Firstname
Poste Restante
Central Post Office
City/State/Province/Whatever
COUNTRY
Ideally, however, you should contact a local post office in the city where you'll be, and ASK them A) if they hold mail, and B) how it should be addressed. This will save you the trouble (and believe me, it can be a LOT of trouble) of attempting to locate the "central post office," if in fact one exists. (I was told in Glasgow, Scotland that there WAS NO "central post office," and that any mail addressed to Central Post Office would probably go to Post Office X. I went to Post Office X, and was told to go to Post Office Y. Post Office Y told me to go to Post Office Z. Post Office Z told me that I was a total idiot for having mail sent to someplace that didn't exist, but they said they'd check anyway to see if I had anything waiting. Two letters, no packages. I was waiting for three letters and two packages. When I told them how big the package was, they suggested calling Parcel Force, which is a totally separate company which deals with packages. Parcel Force said that they had no idea, and told me to call another number. I called the other number, and they said they had no clue, that I'd have to get a tracking number. I called home and attempted to get a tracking number. I called Parcel Force and gave them the tracking number. "That's not a tracking number," they insisted. They finally gave in to my pleading, and checked to see if there were any packages sitting around with my name on them. Sure enough, both my packages were sitting right by the phone. "You're lucky," I was told, "these were about to be returned to sender." I never did get the third letter I was waiting for.)
Half my reasoning for getting an American Express card was so that I could receive packages at American Express offices. It turns out that, not only can ANYONE receive mail at AmEx offices (it's free if you have a card), but they do NOT hold packages! They will hold LETTER AND TELEGRAMS ONLY! You can get a list of AmEx Travel Service offices (not all AmEx offices are Travel Service offices, and only the TS offices will hold mail) by calling AmEx. The only number I know for them off the top of my head is 1-800-THE-CARD (1-800-843-2273).
One advantage of being an American Express cardholder is that, if you have a letter sent to an AmEx office, but it doesn't arrive before you're ready to leave, you can ask them to forward it to another AmEx office of your choosing, at no cost. I have yet to utilize this service, but I hear it works.
I believe that some other travel service companies (such as Thomas Cook) may hold mail also, but I haven't ever checked. If you know the answer, please email me.