Ethernet shield from 12V generates too much heat (the regulator and the surrounding area/parts get too hot to touch). But according to the Mega2560 specs, the voltage range can be 7-12V. I think this spec is not completely true. 12V may work powering up just the mega board but not with anything else attached to it. This should be stated somewhere as this may cause a safety hazard.
I wouldn't be keen on running my Arduino gear on 12v, and would be looking at a dual output PSU if 12v was demanded for other purposes. Having said that, you could be over-reacting and a good solution is to stop touching the things that are hot. If it was a serious problem, it would be common knowledge by now. And don't expect it to run cool on a 9v supply either. My Mega setup is too hot to touch with a 9v supply but has been running more or less continuously for weeks.
You might check that your 12v supply really is 12v. I have one labelled 12v but is really 15v, and that would be stretching the friendship with a 5v Arduino.