Start with one, very well intentioned Safety Outlet Cover. Please ignore gross spots on safety outlet cover, it was after all in use for 6 years before it caused any trouble. And with twins, well, who could possibly be bothered to scrub spots off of outlet covers for goodness sake! Here's a link to a new one - not that I'm suggesting you buy one. Just so you can see what they look like clean.
We installed a couple of these around the house when the girls were little, to keep them from yanking plugs out of sockets, and from sticking things in the electrical sockets.
And then we plugged things in behind them, attached the protective cover, and forgot about them. For 6 years. Then one day last fall, we smelled smoke. Not enough smoke to set off the smoke detector, but enough so you could smell it. It smelled like burning dust, like the first time during the winter that you turn the heater on, only a little stronger. But we couldn't place it. The smell came & went, and although it was disturbing, we couldn't identify it's source.
Until one day, Laura bumped into this outlet safety cover, and jarred it loose. We thought since the girls were 6 now, I would probably be OK to remove the cover, so rather than try to tighten it, we removed the cover. And this is what we found behind it:
Apparently the power brick / transformer thing we'd plugged in behind this "safety" cover had come loose. The metal of the plug was resting on the plastic of the outlet, and every time we turned this particular light on, the metal got hot and started to melt the plastic and burn the dust, etc... that had settled in there.
Here's a shot of the offending power brick after the safety outlet had been replaced with a regular outlet. Amazingly, the power brick was completely undamaged.
I went ahead and hired an electrician to replace the outlet, because I was afraid there would be more extensive damage to the wires behind the outlet that I couldn't see. Fortunately there wasn't. So.... if you've got any of these types of covers in use anywhere in your house - I suggest checking them on a regular basis, and definitely NOT plugging any heavy brick-type plugs into them!