Several of my friends spent years overseas doing just that. They obtained working visas (or the equivalent) in the countries they visited, and traveled the world doing IT work interspersed with hiking, hitchhiking, camping, and whatever else took their fancy.

If you have a knack for writing, you could run a travel blog, write for a publisher like Lonely Planet, etc.

There are many, many ways to achieve those goals that don't involve joining the military.