The Gakken Mini-Theremin is an very basic theremin toy that you can build - but it, amazingly, can actually make music - as Ken Moore demonstrates above.
For my wife's baby shower our friends Sarah and Mika got us a tiny Gakken Theremin so we can get our girl a head start as the next Theremin virtuosa. It's a fun but very sensitive instrument, and since Sidney can't even get her hand in her mouth yet I'll wait a few more months before starting her lessons.
You can find more information on the Mini-Theremin at Maker Shed.
Gaz Williams has one and he brought it round