I certainly appreciate Wayworm's estimate, but I think it might be a bit high for the average young traveler. I don't consider myself a budget traveler by any stretch - the closest I've come to a grocery store on a trip is to stop in for a drink! - but I've never spent $78 a day over a two-week stretch. At that budget, for your trip, I think you'll be able to rent a car every once in a while, get the occasional single room in a hostel, and take in a few activities.
To my mind, the three biggest things affecting cost once you've chosen your destinations is: how fast do you travel? How many activities do you want to do? How often will you be pounding back beer? Quick travel, activities and beer will add up. If not, then hostels will run you $2-$30 pretty much anywhere, you can eat for $10 almost anywhere, and it's a rare museum that will set you back more than 10 bucks.
That said, two final notes. First, wayward is totally right when he says that it's nuts for people to travel halfway around the world on a budget too tight for minor changes. If you're offered a spot in a 4WD to a desolate canyon for $70/day, do you want to turn it down because of money? You've already flown halfway around the world! Second, pre-trip costs are more than you think. It's very easy to spend 6-7k on airfare, insurance, visas, health care and equipment if you're taking in a number of continents, so don't forget that bit.
