When it comes to modern travelers 2-3 months is the estimated time period you should pull from your calendar if you want to make a satisfactory backpacker journey or trip round the world. You can do it faster but your travel experiences would suffer gravely. Most people estimate between 3 months and a whole year to complete this project. Naturally, it depends on the number of destinations; the time spent travelling over land; working periods etc.
Generally speaking, it takes two months to really get to know a continent from the inside out. If, for example, you're backpacking across the Asian continent from Hong Kong in the north through Vietnam, Cambodia, Thailand, Malaysia and Indonesia and all the way to Bali in the south, you might be able to do it faster but then you end up spending all your time on transportation. It's also possible to do a round trip of Australia, route 66 from coast to coast in the United States or a motorcycle trip from Patagonia to Colombia in about two months. If all you want to see is a single city or a single country, naturally you don't need as much time.
It is a good idea to fly as much as possible if you don't have much time on your hands - otherwise you end up spending all your time on local transportation and will probably grow more and more frustrated as time goes by. On the other hand, if you have enough time to spend it's a good idea to travel as much as possible over land (and not by plane) in order to really get to know and a feel of the countries, places and local people. Naturally, exactly how long your backpacker journey should last, will also depend on your budget!