Go into 'preferences' (you can open it by pressing 'Ctrl' and ',' down at the same time on a PC, sorry don't know shortcut for Mac). When the 'preferences' box opens there should be a number of tabs along the top of it, go into the one called 'store'. There should be options on this page and somewhere, the options for 'automatic downloads'. To stop all downloads make sure that 'music', 'apps' and 'books' are all unticked. Then click 'ok' and you should stop getting the downloads.
Hope this helps!