Children enrolled in a course with a certified instructor can get a learner's permit at fifteen (six months earlier than without the course).  At sixteen, children can get a license if they have both parental permission and proof of passing a driver's education course.  Under current law, that course must be taught by a certified instructor; some homeschoolers are interested in seeing that change.
It is my opinion that parents should teach their children to drive, regardless of whether the child also takes a state approved course.  Preschoolers should understand the accelerator pedal, traffic lights, and what makes that ticka ticka sound when we turn.  At elementary age, they should be reading road maps.  At middle school age, they should understand the need to drive defensively:  they should be able to identify cars operated by unsafe drivers, know that as the light turns green, a good driver is verifying that cross traffic has stopped (or is stopping), and know how to compensate for the dangers of the Narrows Bridge.  Finally, when the time comes at 15, 16 or 17, parents should be providing the extensive driving experience they need before they can independently operate a vehicle with confidence-- both our confidence and theirs. 
Here's a closing thought from the National Driver Training Institute's web site:

Maturity affects the choices a driver makes every time he is behind the wheel. Becoming 16 is no sign that a teenager is mature enough to drive! Assessment of maturity is critical in the teen world of peer pressure, poor drivers, road rage, feelings of immortality, and the real possibilities of auto fatality and serious handicapping. No one but a caring parent can accurately assess the maturity level of a young driver, decide when the teen is ready to drive, and then enforce safe driving rules.