This machine takes coal and makes a redstone signal out of it. It uses a powered minecart, detector rails, pistons, and repeaters to do this. The minecart moves around the track once you've powered it using coal, then as it passes across the detector rails the piston cuts the redstone signal (so if the cart were to lose power on that rail you would no longer have power being generated). The repeaters are set so that the signal remains constant at the top of the machine.
Heres a video of the machine working (the lights at the top on the output lines aren't actually part of the design, there simply there for the purpose of this video). The quality isn't very good on this video however.
It'd be useful for a timer which needs to last a certain amount of time (each piece of coal adds 3 minutes to the time the machine is operating). So using that you could use it as a timer.
Another use would be for roleplaying maps basically (if you wanted power to have to be generated by using coal). Or even just for giving coal a new use and more reason to collect it (as people tend to end up with too much coal).
The only problem however is if you get too far away from the machine while it's running it freezes in an on state (so even if the cart stops moving power is still given to things connected). To fix that you need to break the detector rails and replace them (or the redstone connecting the detector rails to the rest of the machine; not sure but I think it's the detector rails you need to break).
As for the reason I built this; someone on the forums suggested coal powered generators be added to Minecraft, so I said that it can already be done (so I went ahead and built one).
I've also heard you can make a redstone signal using a normal furnace (cuz the block updates so you can use something that detects that and then make a redstone signal out of that).
It would be as simple as hooking up a T-BUD to a furnace.
Edit: The problem with that, however, is that you would actually have to burn something with the coal in order for the BUD switch to activate and deactivate. You would also only get 80 seconds with each piece of coal instead of 3 minutes... But you may want that if you're using it as a timer.