I've done this for close to two years, mostly through Latin America, but not necessarily as a lone freelance web developer but building a company along the way, meeting great entrepreneurs and building a stellar team that now spans from Mexico to Argentina.
Some tips (applicable only in developing countries):
Networking with the locals:
Almost every country has an entrepreneurship community of some sort, I'd recommend not necessarily taking the I'm going to be working from a remote beach approach but instead, plug in to every community you can as you travel. Expanding your network with talented people is immensely beneficial for work you are doing for clients or your own startup.
There is usually two or three people that are like the godfathers of every tech/startup community in every country/city, and they are usually easy to spot, as they are the ones putting together the barcamps, the coworking spaces, and any other events. Oh, and most of the time, they all speak english anyway, so language is never a barrier in the tech world.
You can make these connections even before your trip begins. I highly recommend signing up to the http://startupdigest.com/ of the city you want to travel to and find out who is the person putting together http://wiki.coworking.info/w/page/16583831/FrontPage coworking in that city, and the http://barcamp.org/w/page/402984/FrontPage Barcamp.
Living:
I don't recommend making living arrangements remotely (before you arrive), usually what I do is stay at a hostel for 2 or 3 days, and dedicate those days (usually weekends) towards finding a furnished place + wifi to live in. Craigslist is sometimes not as widely used in some cities, but the people that want to rent to foreigners/expats usually find out that craigslist is the best way to find us (and charge us more). Frequently, you'll find that the local newspaper/mediamonopoly has more traction than craigslist or there is a local flavor of craigslist that can show more results. Airbnb is also an option, but usually more expensive.
Often, you'll find that expats are more helpful at finding places to live than locals.
If you are a guy, packing light should'nt be an issue. All my belongings fit in a duffel bag (clothes) and a bookbag (electronics), I'd suggest packing enough clothes to last you a week, the rest you can buy when you get there.
Money/Banking
Before you leave your home country, call your bank, and let them know that you will be traveling indefinitely. I've had my cards suspended so many times because I did not "notify" them that I was traveling, until I had to walk into a branch and just say "Look, I am never NOT traveling, so don't ever put holds on my cards because of that"
Still though, take enough cash with you so that you can at least survive for a week using only cash, just in case you have issues with your cards when you arrive. Buy the local currency as soon as you get to the airport, and some common sense travel tips: Don't put it all in your wallet, put some in your wallet, so if and when they rob you, you can hand them your wallet with some cash, none of your home-country ID, and one credit card that you can easily cancel. The rest, distribute it in other pockets, shoes, inside shirts, etc., and unless you are going to EU/US/CA/JP/SG please oh please don't travel with those enormous mountain hiking backpacks, they just make you an easier/visible target.
Make sure someone back home can get your official mail in the event something happens (lawsuits, banking, subpoenas, citations, etc..) and can send you remittance cash via Western Union or Xoom in the case of an emergency.
You can also pick up clients at your local destination as long as you bill them from your home country's company (you DO have a company set up for your freelancing, right?) It's a bit more accounting work on their end, but not a deal-breaker if you are really good.
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Actually, I think I could go on into more details, but they'd start varying depending on what part of the world you wish to travel to. So I guess, to be more precise, where do you wish to go?