Back in the 90's there was some debate about requiring small children to have their own seat in airplanes. I think there had been media coverage of lap children who died in a plane crash, while some other children in the plane were saved by their seatbelts. Anyway, the idea was that if we don't allow lap children in cars for safety reasons, we obviously shouldn't allow them in planes.

That reasoning sounds simple, but it's actually wrong. While child restraints would make flying slightly safer, flying is already very safe, and so the larger effect of the proposed regulation would have been to make flying more expensive for families with small children. That would have led more families to drive instead of flying, which is much less safe, and as a result more children would have died in car accidents than were saved in plane crashes. Luckily that particular regulation never became law.

http://www.cato.org/pubs/briefs/bp-011.html

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For another very quick example, Congress created the Interstate Commerce Commission in the late 1800's to prevent railroads from using their monopoly positions to exploit customers. But throughout its lifetime, large railroads used their influence over the ICC to control their markets and reduce competition.

http://en.wikipedia.org/wiki/Interstate_Commerce_Commission#Criticism