Makey Makeys are very safe! Since Makey Makey is powered through a USB connection, there is no AC current. The voltage is similar to that provided by 3 AA batteries (50 microamps). This is enough electricity to have fun, but not to harm. I've never been harmed by a Makey Makey and I do not know of anyone who has ever been harmed by a Makey Makey.
Often, educators use Makey Makey with water. Usually mixing electricity and water can have unwanted repercussions. Due to the low voltage and power source of the Makey Makey, it is safe to use water as a controller for Makey Makey (as seen in the numerous videos wherein people are making various controllers using water and Makey Makey
Makey Makey is a very durable learning tool. Having said that, heavy handling and/or misue of the back of the Makey Makey board could impact functionality. Avoid touching the back of the Makey Makey board when possible, and always use on a flat, clean, and dry surface. Consider it on par with the old-school compact discs: You don't really want to touch the disc too much, but you sometimes did and it was okay. ;)