Lots of comments about heat, but no one has correctly answered the question.
ALL forms of vegetable oil and vegetable oil derivatives, which both PG and VG are, produce formaldehyde when they reach their smoke points. That is, when the liquid reaches the point where it begins to smoke the smoke will contain formaldehyde. Obviously this would be very bad for anyone vaping. No one vaping would ever want to puff on a product that is producing smoke rather than vapor. The temperature required to make that chemical conversion is far hotter than anyone using an ecig would be comfortable inhaling from. Not to mention it would burn up most wicking materials and would cause some like cotton to burst into flames.
Formaldehyde production is really a non-issue in ecigs. It doesn't happen. IF there is any formaldehyde produced at all it's in such a trace amount that it's unlikely to be harmful, and is far below the amount produced when burning tobacco.
If you're looking for something to be worried about in ecigs, be afraid of juices that use diacetyl as a sweetener. Long term exposure to inhaling diacetyl can cause Bronchiolitis Obliterans (Also known as Popcorn Lung), scarring of the lung tissue which is irreversible, and has symptoms very similar to COPD. So if you're worried about your long term health try to avoid flavoring agents that include diacetyl.