If you want to circumnavigate the globe relatively cheaply, I would advise getting a 'round the world' ticket - any good travel agent can advise you on these and you can get a six to eight stop ticket for under 1000 pounds (1500 euros).
Each leg of your 'round the world' journey does not have to start where the one before ended: for instance you could have one leg of your journey end in Bangkok, then travel south overland through Thailand and Malaysia and then fly out of Singapore on the next leg of your journey a month or two later.
This means (especially in Europe and North America, though as Al says, it's more difficult in Asia and Latin America or indeed sub-saharan Africa) you could take several low-cost flights to travel around from country to country before resuming your 'round the world trip'.
Again, as Al mentions, you'd need to book the low-cost flights well in advance in order to most benefit from cheap prices.
I'm about halfway through developing a European low cost airlines comparison tool on attitude Travel:
Basically, the better prepared you are, the more likely you'll be able to relax and enjoy your trip!
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I was reading below about a guy who travelled europe on cheap flights, and its quite inspiring for me.
I would like to travel the world, in no specific order, maybe completely at random, based on cheap flights available at each point. I would like to do this for maybe a year, or maybe longer.
I am totally inexperienced here, I have travelled to a few european cities, but that is all, and know I will be out of my depth here!
Has anyone any tip, links, ideas, or anything for me? I am thinking of leaving in the autumn.
I am quite interested in how people communicate when abroad, I use the net alot, and would very much like to use it abroad to keep in contact/find info etc, so any info on service providers etc in other contries would be appreciated!