In Europe travel was our single greatest expense. We did a lot of walking and sleeping on night trains to cut costs. This pretty much restricted us to city centers. In Asia travel is cheaper. Even for short trips we took buses, trains, planes, motorcycles, tuk tuk's or whatever the mode du'jour turned out to be. Keep your freedom; don't book more than a few days in advance for anything but plane tickets, unless you have to.
For major discounts on international flights plus museums fees and other stuff get an STA card from the Student Travel Association. If you live near a college there's almost definitely a branch nearby. If you ask nicely, the STA agent will give you a card even if you're not a student. They're a travel agency and not affiliated with any schools so it doesn't matter to them. The card costs about $25 and saves you tens to hundreds on every international flight you book through them. Drawbacks are minor: you'll probably have to get your tickets at least 2 weeks in advance, you don't usually pick the airline and you have to visit the office (or the website) based in the country you're departing from to book the tickets. None of this is really much hassel unless you're in a hurry. If you can't wait 2 weeks you're not likely to get cheap tickets elsewhere anyway.
Multi flight tickets are cheap but tend to keep you on a schedule. The World Awaits (pg. 77) shows cheap links from country to country. Shop around for good deals. Get a travel agent who specializes in budget travel. When booking, follow major airport flight paths directly to lower cost. Call around. Find an agent whose been where you're going and get them excited about your plans. Sunday newspapers often feature great ticket discounts. When I went to Thailand the first time I found cheap tickets by booking through a Chinatown office. They get good rates because of the volume they handle to and from Asia. "Lucky 8's for you. You pay $888 loun tip!" Also, check the phonebook or local colleges. Type the keywords "student, budget, discount and adventure" into a browser and see what comes up. Courier flight info is available at IAATC and aircourier.org. Rail and other passes are often not available in the country you want them for because they are only for foreigners. Check underground travel for details. Railpasses don't seem worth it to me but here's the link anyway.