I'm planning a journey during my next vacation in Febuary 2013 from São Paulo to Paris. In one of my researches, I found a good flight option with KLM. The plane stops for 6 hours in Amsterdam (Netherlands) with all fees/taxes included. My doubt is, will I need to pay another boarding fee if, during this stop, I get out of Amsterdam airport to visit the city? Last year I did the same with TAP in Lisbon and had no problems with it.
No, you will not need to pay any additional fees.
Any applicable airport tax will be included in your ticket and is irrelevant to whether you spend the entire 6 hours inside Schiphol's security zone or if you use some of it to venture outside the airport.
It is entirely at your discretion how you spend that time. Just make sure you are back in time to pass through security in time to catch your flight.