I like thinking about the world before electronics. Not that I'd like to return to those days, but the machines invented to perform tasks in the world of mechanics are sheer brilliance. Probably topping the list of really cool mechanical machines is the machine known as Archimedes Screw.
Archimedes Screw enables water to be drawn up hill (or to irrigate some Hanging Gardens that might be hanging around the city of Babylon). How does it work? Well, you turn the screw and the water flows up the screw. The simple machines that you learned about in elementary school? Well, here is where they matter. The screw is an inclined plane wrapped around a cylinder. As the screw turns, it scoops up water. This water is pushed up the incline (around the cylinder) until it finally pours out from the top, feeding an irrigation system.
Does such a mechanical system still have value in today's world? Of course! Not only is it fun to create your own irrigation system from the local creek (a fun weekend project), but such systems are of wide use in the world - from the developed world (where Archimedes Screws are used in sewage treatment plants - like the one in Memphis, TN, shown above) to the undeveloped world needing cheap, available irrigation (shown below)
For more on Archimedes Screw (and his other wonderful inventions), check this out.