Click the picture for a larger version. You may also want to see a picture of the entire rig.
This is a variant of WB4LFH's "very simple FET regen", powered by four cells of baking soda, old Swedish 5 öre coins, and iron wire. I actually heard an FM station clearly, as well as several CW and AM stations. The battery voltage is between 3 and 4 volts unloaded, but since this receiver uses a few mA, it drops down to around 1.5 volts. Running out of power? Just shake the battery a little!
I made the following modifications on the original schematic: first I connected the antenna to the tank via a small capacitance (in the order of a few pF). Second, I put a 1M grid leak resistor from the sillicon tube (MPF102) and connected it to the tank using a 27pF capacitor. I skipped the capacitor across the earphone, which, by the way, is of a 1k ohm resistive type.
The project is rather cheap. If you look at the parts list below you'll see that the total cost - including a large supply of baking soda and the earphones - amounts to about three dollars. Mouser electronics has all the parts, although with shipping you're probably better off digging through your junkbox (or that of a friendly electronics geek).
Where to go from here? Since regenerative receivers radiate RF, you could make a baking soda-powered CW transceiver in the QRPp class. This battery type is not exactly good, improvements could be made, but its simplicity is hard to beat I think.