A Joule Thief (JT) is a step-up voltage transformer based on the working mode of a PWM (Pulse Width Modulation), it produce a oscillation in a inductor with the help of a transistor (2N3904, 2N2222, ...) then the output of the inductor is your new voltage. The result is that you can light a white, blue or even a ultraviolet LED with a single 1.5V cell (AA, AAA or any type of cell, i have used a watch cell too). This "voltage booster" circuit is not very efficient but it can use batterys that are near depleted. I whud not power up a microcontroler are anything that whud be disturbed by the voltage and power oscillation of the output, there are some dedicated step-up voltage boosters like the IC from Maxim with a 90% efficiency. With a bigger inductor and another transistor it is possible to get some very high voltage, i have see on the web some JT that can light up a neon tube from a 12v bike lead acid battery.
I connect multiple LEDs in parallel and they all light up fine, as long as the LEDs are from the same maker and made about the same time. The Joule Thief's pulsed output helps distribute the current evenly over all the LEDs.
In my new instructable (hope i will upload all stuff this week) i gonna show ppl how to have a JT with a battery drain of 2.60 mA.
The transistors i listed are very cheap the 2N2222 (250Mhz) in plastic package is realy cheap, and the 2N3094 (300 Mhz)