Well, it's pretty simple for me.
Traffic accidents, to use Clive's example, have a cause, and for that reason should, perhaps, not be called accidents. They are accidental in the sense that noone involved had an intent, but they are not accidental in the sense that there was no cause for what happened (a driver ran a stoplight while looking the other way).
It was not accidental that the city of New Orleans was flooded, but was caused by the difference between the force of Katrina and the resistance forces of the levees.
The shape of a cloud is not accidental, but the result of laws we can barely understand.
Someone wets the bed accidentally in the sense that there was no intent to wet the bed, but not in the sense that wetting the bed had no cause, apparent or otherwise.
So I want to define the accidental primarily as an event that falls outside of intent.