I've always kind of been interested in just leaving and becoming totally anonymous...to me it seems like a huge undertaking though

so look, being anonymous in a single country is one thing, but in many countries...that makes it much harder.

First of all consider the id you'll need...United States you'll need birth certificate, SS, Drivers License and anything else you can think of... now the fact is none of those are too difficult to get ahold of or to change if you know the right people or know what you're doing.

Now as for travelling, you have to have the balls and the knowledge to know how to get a fake passport or to get a legit one with fake info in it, and any kinds of papers you'll need for other countries. You'll probably need to know how to speak a few languages if you intend to spend any amount of time in foreign countries.

Lets consider transportation too, you could get a fake drivers license and you could acquire a car (I say acquire because the fact is you could steal one and repaint it and fake license plates are a must). I wouldn't plan on driving a fancy car though, the cheaper the car the less attention it draws. You'll also need fake license plates...without them you'd have to get insurance to register your vehicle. Now with a fake license plate, I'd personally invest in the best radar detectors and scramblers I could find. With fake docs and a fake plate getting pulled over could end your fun.

What are you going to do about money? Traveling can be expensive. In all honesty...you can steal most anything. Need gas? Get a siphoning system and a large gas can. Need food? It takes little thought to come up with the limitless places you can get food for um....your own special price. Plane tickets? I can't say I know enough about that, but I know there are a lot of sites that list tickets that you can get for cheap so the airline can fill the seats. The fact is you'll have to be packed and have a way of getting to the airport quick for those.

So you're opposed to stealing? Consider the all the illegal substances out there that people are dying to get their hands on. Even better...make your own money. Counter fitting, with all the new technology nothing could be easier.

I've just scratched the surface on all the things you need to think about. The fact is you could do it in a nearly legal way...get a good education and work hard most of your life living with only what you need to get by. Save your pennies and when you have the money just go travel anonymously.
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