strawdog \ Limelight
The Joule Thief is a well known circuit for boosting voltage from a nearly dead battery to power an LED. What if you don't have a dead battery? Use a lime, and some copper and zinc!
This was a surprisingly educational project. The Joule Thief circuit is extremely simple
Wikipedia:Joule Thief
Here is the result, hooked to the lab power supply, with 0.5V input, and basically unlimited current.
LimeLight/limelite_circuit.png
The circuit for the LimeLite
0.5V btw, is not enough to light an LED, even a red one. The result is nice and bright, and the scope hooked to the + side of the LED shows an approximately 2kHz roughly square waveform.
LimeLight/scope_slow.jpg
The signal on the LED lead with 0.5V from a bench power supply.  About 2kHz

A battery can be made from any acidic substance – like lime juice – by placing two dissimilar metals in it. Copper (A wire or a penny) and zinc (a galvanized nail) work well. However, just sticking copper and zinc in a lime will generate a voltage, but it can't sustain current for any length of time. As a result, it won't drive the Joule Thief. The animation shows what happens though
LimeLight/scope_anim.gif
What happens if you naively stick metal in a lime

If you just stick two pieces of metal into a lime, the internal resistance of the lime means that the available current drains very quickly. The circuit switches faster and faster as the lime battery cannot recover.
One solution – soak tissue in lime juice and wrap the galvanized nail. Then wrap that with copper wire. This works better.
LimeLight/tissue_battery.jpg
A battery made using tissue. This generates a reasonable amount of current to drive the circuit.

A better solution – shred the inside of the lime. This lowers its internal resistance caused by the membranes of the lime, and allows enough current to flow to operate the Joule thief. The current available is still significantly less than that for the lab power supply though, and it switches at a noticeably higher frequency - something around 10kHz.
LimeLight/lime_battery.jpg
Limelight driven by lime based battery
LimeLight/glowinggreen.jpg
Limelight driven by lime based battery

Many thanks to FX for the high efficiency diodes – works much better