One thing I used to do with them when they were a bit older (3yo) is change the batteries of their own toys (by that time they were a long way from the phase where they put everything in their mouths).
They had a blast picking the screwdriver, twisting the screw with the appropriate amount of force pushing down on it, fit the tip on the screw gap, twisting it in the correct direction and learning something so simple as to find the correct sides of a battery (butt, nose), inserting it in the correct way (butt first on the spring) and pushing down but holding it so it doesn't jump back at you. They took quite some time to get this right, but it helped a lot with something I only learned existed after I had kids: fine motor skills. A two year old needs that as well - that's why they tend to be so destructive with delicate things, since they don't have precise control over their own hands (I picture a poor electrolytic cap being ripped apart from a dev kit because it is bright yellow and shiny...)
Another thing I used to do with them is to grab a small power supply (or sometimes batteries), a bunch of LEDs and small computer fans, a few switches and put together simple stuff such as turn on a lighbulb or the fan. We don't think anout it, but it takes a great amount of skill to properly press the J clips or alligator clips with their tiny fingers, have the appropriate amount of strength and control to press it without skipping from their hands and properly put it in the wires.
Anyways, I learned that so many things we take for granted are learned and not innate (such as knowing where your nose is, for example) that I have a lot of fun developing the firmware and programming this empty flash memory of my kids' brains.