Less than you think. Following is from graphs in the Boeing publication 747-400 Airplane Characteristics for Airport Planning, dated Oct 1994:
Sea level standard day (59 deg F, 29.92 inches Hg), no wind, level runway, air conditioning off (except one pack can be powered by the APU), PW4056 engines: minimum runway length of 5500 ft allows a takeoff weight of 635,000 lb, 6000 ft allows 665,000 lb, then a fairly straight line from there to 10,100 required feet for 850,000 lb. These are runway requirements, which are of course longer than the ground run.
Same publication gives payload-range graphs: it seems that aside from runway strength problems a 744 could carry 400 pax and bags (but not much freight) off of SNA's 5700-ft runway nonstop to New York, or the same payload out of LGA's 7000 ft to Europe. That includes reasonable reserve fuel.