The NHTSA undertook a two-and-a-half year study that examined 5,471 injury accidents nationwide in order to figure out how accidents were being caused. Government researchers conducted their own evidence gathering at crash sites in order to establish a first-hand account of causation. What did they find? Among other things, that more drivers crashed as a result of crossing the center line (11%) than as a result of speeding (5%). Speeding, in this case, defined by "too fast for conditions," not necessarily above the posted limit.
In accidents where driver error was the cause, speeding also came in last as a causative: the 8% who drove too fast were tied with the 8% who fell asleep or had heart attacks while driving. What's more, the NHTSA's causation percentages are strikingly similar to the percentages found in an independent study conducted by the Virginia Department of Motor Vehicles. In its study of crashes in 2007, the VDoT found that 2.9% were due to speeding -- dead last -- while 3.8%t were due to drivers falling asleep or falling ill at the tiller.
Interesting info regarding driving speed and auto accident fatality from Autoblog