Where can I find a database of historical wildfires in the USA back to 1960?
I would suggest the National Interagency Fire Center, which keeps statistics in a variety of formats as well as lists of historical fires.  For instance, you can see a list of historically significant fires as far back as 1804 here.  In general, the closer you get to present, the more information about fires there is.  

Other websites with historical wildfire lists include:


Wikipedia list of large fires
USGS spatial data back to 1980 with a viewer here
NOAA World Data Center