Why do weeks start on Sundays?

Officially, on calendars and such, the week begins on a Sunday. Was there a logical reason for this in the past? Does any logical reason still exist?

Since we generally think of ‘weekdays’ (Monday through Friday) as being followed by ‘weekends’ (Saturday and Sunday), it seems like it would make much more sense for the week to begin on Mondays and end on Sundays. Should we change it? What kinds of problems would such a change cause?