I realize that some countries might have mandatory government-regulated driving courses before you can get a driver's license, but I think that most countries allow parents the option of teaching their children to drive. Assuming the option is available to you, what are the pros / cons of personally teaching your teenager to drive versus putting them in a driving course?
I was not aware of countries that allow driving lessons exclusively by the parents.
I do know that both Sweden ("övningskörning") and Austria ("L17") allow the parents or legal guardians to provide training in theory and practise from age 17 (in Europe, 18 years is the minimum age for driving). But these trainings are only preparatory; there must still be formal training by professionals in both theory and practise, though less of it.
I had such preparatory training and needed essentially no practical training, but the theoretical side was sorely neglected! I think this parental preparation has good and bad aspects, directly linked to the parents' driving (and teaching) skills.
Good: More preparation means fewer driving lessons means less money spent.
Bad: There are bound to be some bad drivers, or adequate drivers with a few bad habits (aren't we all?), and they would unknowingly pass on bad habits. Just like in any other discipline, the driving instructor must spend time to unteach these bad habits...
Also, consider that professional driving-school cars have extra mirrors and brake and clutch pedals for the instructor, which private cars don't have - so private training is a matter of safety consideration.
Since private cars don't have these extras, you can't easily prevent accidents. Make sure that the car is fully insured (comprehensive cover, rather than partial coverage) and that the maximum cover is very high (Austria rel 10 mio. €!).
In summary, I would say that some private training is a good and cost-effective beginning (provided there are no accidents) but I would recommend professional training even if it's not necessary, because we are just users, not professional trainers. Do you really know all the traffic laws? Those that are valid in 2011?
I know it is common that we think we can teach our kids to drive better than some school. I know I feel that way myself. However, studies show that kids who learn from someone other than their parents tend to do better on driving exams. Of course, this could simply be a manifestation of the Dunning-Kruger. The state where I live has Driver's Ed available in high school, so my children will take that. But I will also teach them myself.
Here is a link to one study: (large pdf warning) http://www.nhtsa.gov/DOT/NHTSA/Communication%20&%20Consumer%20Information/Articles/Associated%20Files/parent-taught_driver_ed.pdf
If you go to the NHTSA home page and search for parent-taught there are others as well
Driving is difficult, particularly when one is just learning, and is exceptionally dangerous. The likelihood of your being better able to teach it than someone who does so for a living is virtually zero. Even if not required by your jurisdiction, get professional training that includes supervised time behind the wheel.
Take the time and find a good driver training school. There is loads of information available about the schools on the internet. Go see the local police and ask for recommendations. Ask your insurance company for recommendations. Find the best school you can, because it might end up saving lives.
When my daughter was learning to drive we enrolled her in a school that employs California Highway Patrol officers. It was a tremendous experience for her. Three years later, she still remembers the lessons, uses her mirrors properly, and is very defensive.
But my wife and I also spent a lot of time in the car with her driving. We spent at least 20 hours with her for every hour she was in driver training. We reinforced what she learned in driver training, and when we were comfortable, we allowed her to get her license.
In the UK there is no requirement for a professional to teach your child, however they must sit the test with a professional. I started learning to drive very young, so by the time I was 17 and allowed to drive on the road I had a few lessons with my dad and a couple from a professional to confirm that I was learning the right things.
I think as long as you are a good teacher and a good driver, you should be able to provide a reasonable start for your children. Definitely get some advanced training though - in the UK we have the Institute of Advanced Motorists - the equivalent will help you get to a position to guide your children correctly.
I am a firm believer in teaching them well before they are allowed on the road - I provided mine a cadet licence for karts at age 8 (the minimum hereabouts) so that they can get the car handling practice embedded before they need to think about learning rules of the road and all the other complications of on-road driving.
I realized there was one important aspect of the question that nobody else hit on, so I felt it appropriate to provide my own answer.
While performance on a driving test and cost savings are important factors to consider, I think a more important factor is that as a parent you personally feel comfortable letting your child drive.
I want to be able to know that over a period of time, my child is driving responsibly and defensively. I want to feel that when I let him drive on his own, he is going to stay calm, follow the rules, and be courteous. I feel that the best way to gain this trust is for me to teach and observe my child over a period of time. Letting them get instruction from someone else, won't give me the same sense of comfort.
Among other reasons, this is why we've decided to do the driving education ourselves.