I travelled for 1.5 years. It cost about the same as living in a US city did for me.
Here are some suggestions:
== Transportation ==
1) learn how to use http://matrix.itasoftware.com for US flights. It lets you find the cheapest combination in a 30 day range. It also lets you search from: BOSTON or NEW YORK to CHICAGO or LA. In other words, it lets you take advantage of your flexibility. ITA Software is the company that does the heavy lifting for most of the airlines. The interface is hard to get used to, but it's worth it.
2) break your flights up. For example a one way NYC => LAX and then a one way LAX => Sydney Australia is *cheaper* than NYC => Sydney (will probably layover in LAX). In general, if you have a layover anywhere, you should instead be flying there, hanging out there for a few days, then flying the second part.
3) Sometimes buying a round trip ticket is cheaper than buying a one way. Go figure. Just miss the return flight intentionally?
4) Round the World tickets are surprisingly cheap, only a few thousands dollars for many flights between many countries. This is great for planners.
5) http://kayak.com/explore/ -- lets you see at a glance the cheapest places you can get to from any city. You might be surprised which places you can get to from NYC for under $1k.
Flights are expensive if you travel fast, but cheap if you travel slow. Plus once you get somewhere far away, you can stick to buses or hitchhiking or whatever method the locals use to get from city to city.
== Housing ==
1) The best thing to do is stay with friends. Some friends wouldn't be comfortable hosting you, but others would love to have you on their air mattress for 2-4 weeks! You have to feel them out, and be careful to hook them up so both of you benefit from your visit.
2) Hostels are only $15-30/day usually and they let you cook and make it easy to meet people. I like http://hostelworld.com they aggregate all the hostel information and make it easy to book. Go check out prices in the cities you'd like to travel to!
3) I've heard that in SE Asia you don't even have to bother with hostels as *hotels* are only $10/day-ish. I haven't been there yet.
4) When I was in Sydney for two months I went on their craigslist equivalent and subletted someone's room for the whole two months. I got a kick-ass deal and she got to collect rent while she was travelling.
5) http://airbnb.com -- I haven't tried this but it's all the rage these days.
6) CouchSurfing is "free" in theory but will often end up costing you $5-20/day when you buy dinner for your hosts etc., to even out the karmic imbalance. Plus you can usually only comfortably stay for a few days at a time.
It can be hard to get your first surfing experience, as few people want to take a risk on you when you have an empty profile without any references. You should look into hosting in NYC. There will be incredible demand for your apartment, you can wait to be selective and choose someone that you think will be compatible and interesting for you to host. In addition to getting you out of the house on long weekends (!) this will build up your profile for when you want to surf on other people's couches in the future.
The benefits of CouchSurfing go *way* beyond just a cheap place to stay though.
== Misc ==
A lot of the tricks that will help you now will also help you while you travel. If you know how to cook, you can just grocery shop and then cook at the hostel. Actually little routine things like that can be way more fun while travelling for some reason.
Similarly, if you have big holes in your spending now, they'll be amplified on the road. Enjoy dropping $50 at bars? That will happen more frequently on the road. Enjoy eating out? That too.
Pack light. You should be able to fit everything you need into a fairly small backpack (~40L). Then you're much more mobile and incognito, and it's easier to watch over your stuff. With so few possessions, you can really ramp up the quality of each item without much overall cost.
You can look up which currencies the dollar is doing the best against and allow that to influence which country you travel to.
The best book on travel is by Rolf Potts and is called "Vagabonding: An Uncommon Guide to the Art of Long-Term World Travel"
There is a Vagabonding blog, too: http://www.vagablogging.net/
Finally, every major city in the world has a CouchSurfing group with many active members discussing traveling, living cheap, alternative lifestyles, etc. The NYC one is *especially* active. I just checked and it has 38,481 members and 108,484 posts. That's your single best travel cheap travel resource after me!
PS: I don't think you need to save up specifically for travel. If you have a $1,300/mo living stipend from ERE, you can easily make your travel budget fit into that.