Well one thing I remember now which I did with my father when I was maybe 10 or so was to make a miniature airplane (he teaches aerodynamic constructions at local university, so we didn't have to do a lot of research).
We made body of the plane out of a fountain pen, main surface of monoplane out of folded lightweight cardboard, hobby motor to drive the propeller and cardboard to make the tail. We got wheels form toy cars and used small paper clips as axles. Propeller was made out of a piece of 0.5 mm aluminium sheet.
Then we connected it to a base of a vise via rotating joint and a lever. A counterweight was attached at the other side so that the plane side of the lever was just a little bit heavier than the weight side.
We run a cable form the base of the vise to the plane and connected it on the other side with a potentiometer, analogue voltmeter, amperemeter and a wall wart.
Yeah, I know it isn't very electronics related, but it did show relation between current and voltage. It was also very visible that changing voltage could make plane start moving on the table and that changing it even more could make it lift off and control its altitude.
At the time I thought it was pretty cool.
Some of the other things I did was to make electromagnets form pieces of iron and thin cables. They were very simple and not very cool to me at the time, but they could lift small nails and similar objects.
Two things that are simple and could be cool are LED Throwies and LED Floaties. There are also improved LED Throwies which only work in dark, so they save battery energy.
I can't think of anything else interesting at the moment.