In my case, I got lucky in that my parents were keen travellers (and happy to do so on a ludicrously-low budget - we went camping and/or youth hostelling around most of the UK and Scotland when I was a kid). Apart from that, all I can suggest is: * Look at sponsored expeditions - my trip around Malawi by bike, for example, was sponsored (in aid of a charity that provides anti-retroviral drugs in central Africa), and was a fantastic adventure.
* Jump on cheap opportunities - if you see a way that you can cheaply get to the other side of the country/world, even if it means sleeping in a dorm room or in a tent, take it. Better to have the story of how you had to drive through the night to return a borrowed car, after spending the day ice climbing (true story), than to sit at home and surf the web. Make friends in distant places, and couchsurf for one another, if that works for you. Don't know if that's actually any use or not: just my experience!