A lot! I have two planted tanks, and one that is not planted. All my tanks are on the same water change/ cleaning schedule, and Ll have been established for over a year or longer. My 30 gallon didn't have any plants because my blue crawfish just kept destroying them. Just before my scheduled weekly water change, the nitrates in this tank were always considerably higher than my other tanks. I finally threw in some floating plants (brazillian Pennywart) and my crawfish has left them alone for the most part (since they're out of reach).
Since I've added the floating plants, the nitrates have been lowered by about a third.