+1 to removing the clutter of completed tasks during the day. It feels good at the end of the day to see everything marked off as done, but during the day these tasks clutter the view.
An alternate solution to consider: change the sort order so that completed tasks always show up at the bottom of the list. (Maybe: make it two groups of tasks, not-yet-done and done, and apply the sort/group options to each group independently, then put the not-yet-done ones above the done ones. This might avoid the need for a new UI option, while removing the clutter during the day, but still giving us the satisfaction of seeing everything crossed off at the end of the day. The best of all worlds!)
But I'd be happy with the "hide completed tasks" option too. :-)