I’m sure the building codes require a minimum, but I have no idea what it might be.
6:12 in Buffalo, according to this wiki article (IOW, FWIW):
In general, the pitch of the roof is proportional to the amount of precipitation. Houses in areas of low rainfall frequently have roofs of low pitch while those in areas of high rainfall and snow, have steep roofs. The longhouses of Papua New Guinea, for example, being roof-dominated architecture, the high roofs sweeping almost to the ground. The high steeply-pitched roofs of Germany and Holland are typical in regions of snowfall. In parts of North America such as Buffalo, USA or Montreal, Canada, there is a required minimum slope of 6 inches in 12 inches, a pitch of 30 degrees.
http://en.wikipedia.org/wiki/Roof#Drainage