I think the hardest part about getting out there and traveling is getting out the door of your old life. I realized, much as the OP and many of the responders have, that you can either wait until you're older with a good paying job and lots of time off, or travel young and give up on the 'ideals' of home ownership, domestic partnership (unless you have a FANTASTIC significant other), and material goods.
I slowly started getting rid of crap as I moved through my second stint through college. Each spring and fall, I looked at the stuff I had and threw more and more of it away, gave it away, sold it, traded it, or whatever to just be rid of it and didn't replace it unless it turned out to be absolutely necessary. It took about three years, but as it stands now I can just about fit everything I own on my motorcycle or in a smallish box that gets USPS'd to whereever I determine my next destination to be. At around the same time, I got a summer job in Alaska... two weeks later that box was in the mail and the bike was packed, and I moved to Alaska from Maryland. I still have bills, I still have some debt, both of which should be settled by the end of summer I hope thanks to this job, but most importantly I have my freedom.
At 28, 29 in three weeks, I'm finally doing exactly what I want to be doing: working to travel and live.
2008 Yamaha WR250R