Here is a rule-of-thumb I discovered: For each 1.5 volt battery in series, you put a corresponding 3-volt white LED in series on the output, and it works; but start out with a higher-value resistor at first, like 10K or better yet, use a 1Meg potentiometer in series with a 100 ohm resistor.
If you are using red LEDs or any other kind with a different forward voltage, just make sure you at least double the incoming voltage by the total forward voltage at the output.
So, for example, if you were powering a bicycle red rear LED, you could use 4 fresh 1.5 volt AA cells in series at the input, for 4 x 1.5v = 6 volts in; then, you would want 6 red LEDs at 2-volts per LED, 6 x 2.0v = 12 volts out. If you use 7 or 8 red LEDs in series, that's fine, too because the Joule thief adjusts itself -- you'll just have a different resistor for a particular brightness.
Why would you want to do this? Well, I wanted to do it to see how bright I could get it. Also, you can make the light last longer, especially if you start with fresh batteries, and also if you put a potentiometer in series with the resistor so you can adjust the brightness. As the batteries "die", you can actually drain the batteries much further and get the individual voltages much, much lower than the usual 0.6 volts for a standard Joule thief effectively "stealing" a lot more "Joules". That's the other reason I wanted to do it -- I wanted to see how low I could get the voltage (and you can get it about 0.6/4=0.15, you can steal Joules down to about 0.15 volts if you have four AA cells in series.)
WARNING:
When stealing Joules down to these low voltages, I have found that battery leakage and/or corrosion is practically guaranteed. A method has to be developed to protect the electronics when this happens. The three-AAA cartridge in many dollar store lights actually seems to do a pretty good job. Industry standard protection has been implemented in the case of the 6V lantern battery and also the 9V battery. Both package smaller cells into a higher voltage battery, and do a pretty good job of limiting corrosion from leakage. Using AA or AAA Energizer Ultimate Lithium also seems to prevent corrosion/leakage (AAs are the better deal, value-wise.)
Finally, they have 12-volt white LEDs in a single package, which I use for this, so it looks like only a single LED. Inside the one LED, though, are four white LED dies in series. That's what gives it the 12-volt forward voltage drop. Here's a fairly efficient CREE XLamp LED for less than five dollars. You can put 1.5 amperes through it (which means that you won't need as big of a capacitor on the output, perhaps 0.1uF to 1uF). Or this 3-LED strip for 50 cents. Enjoy!
PostScript:
At my local dollar store, a package of two 100W Sunbeam standard household light bulbs costs less than two dollars, and each bulb contains 32 16 volt LED's, which makes them about 3 cents per LED. You can remove them by putting the PCB on a piece of aluminum foil on top of a newspaper, and use a heat gun in circular motion to heat the entire board while constantly testing the LED's with a bamboo skewer to test when they are ready to fall off. This worked very well for me. Four of the LED's are 8 Volt.