This is my version of the LED Throwie. The design isn't mine, this is just my mod of it. In the original design, the LED Throwie is on from the moment you put it together. This can be annoying if you're planning to make tons of these, or if you want to make them ahead of time but not have the battery run out. Someone has already posted a mod that adds an on/off tab to the throwie, however I've taken it one step further: in this design the throwie automatically turns on when it sticks to something, and turns off as soon as you remove it! It's just as simple to make as normal throwies, and doesn't require any extra materials either! These also work great as simple LED pinch lights. Credit goes to everythingdigital for the idea (it was mentioned in a comment), but the implementation is mine.
I'll point out that though this instructable may seem long or complicated at first, it's only because I wanted to make sure it was well documented. It is actually VERY easy and VERY quick to do. Making these throwies should be just as easy, and take no longer than the original design. Once you've done one and you understand how it works, you'll be whipping these out in no time.
From the original throwie:
Developed by the Graffiti Research Lab a division of the Eyebeam R&D OpenLab, LED Throwies are an inexpensive way to add color to any ferromagnetic surface in your neighborhood. A Throwie consists of a lithium battery, a 10mm diffused LED and a rare-earth magnet taped together. Throw it up high and in quantity to impress your friends and city officials.