World's Simplest FM Radio TransmitterLet's assume for a moment that for reasons beyond my understanding, you may want to build a small FM radio transmitter that you can plant somewhere and never come back to - a disposable transmitter so to speak. (Possible scenereo: Your Govt has taken full control of the airwaves with propoganda, and you want to get your anti-message out). You would want to keep the component population count down to a minimum, because you don't want to spend a fortune on it. You also want to make it not waste a lot of energy, as this "disposable" transmitter would also need a "disposable" battery. This is the transmitter for you. With a population count of only 6 total components, easily glued to the back of a 9 volt battery, simple to build - this can be placed just about anywhere and simply forgotten. Of course - the environmentalists, and perhaps the govt agencies might not like it after you planted thousands of these things, but hey - this is a hypothetical design for a hypothetical situation anyway right? 
Here's how it works. Glue a 74L13 microchip ($1) "dead bug" (upside-down with legs up in the air) to the back of a 9 volt battery. Make sure you mark on the underside where pin 1 is so you don't get lost. Now using a small piece of wire (24 guage) solder pins 1-4 together. Solder a short piece of 24 guage wire from pin 4 to pin 6. Do NOT solder pin 5 to anything yet. Also solder pins 9-13 together. Now connect the two rows of pins together (9-13 soldered to 1-4) with some of your 24 guage wire. Solder a 33pF variable capacitor between pins 6 and 7. This will act as your "tuning device". Solder a 100nF capacitor to pin 5. This will act as the audio input to the transmitter. Now solder the "live" tip of your input device (say a disposable MP3 player) to the other end of the 100nF capacitor. Now it begins to get tricky. Solder the ground from the MP3 player and negative side of the 1N5231 (5.1V) zener diode to pin 7, along with the black lead for a 9V battery clip. Solder one end of the a 10uH coil and (aprox) 10 feet of copper wire to pin 8. Now solder the other end of the coil to pin 14 on the chip, to the positive end of the zener diode and to a 100 Ohm resistor. Finally. solder the red lead of the battery clip to the 100 Ohm resistor.
Operation: Go to your transmit site (preferrably the top of a hill - with a small tree on it). You may want to take a small FM radio with you. Throw the 10' wire into the tree (your 2 wavelength antenna). Plug your disposable mp3 player into the input, and play a looping song, program, or message. Plug the battery in, and listen for the program on the radio. Tune the 33pF variable cap for the intended frequency. Walk away and don't ever come back. Another interesting place to put it might be the overpass of a very busy (rush hour?) highway. In this case, connect the ground to the guard-rail, and hang the wire antenna down off the bridge - preferrably not into traffic - say along one side of the overpass. Would be easier to do this along the side without being seen anyway. Not counting the MP3 player the whole setup should cost less than $5 to build. I've seen MP3 players as cheap as $3 each - so the whole disposable set up is less than $10 each. As a side note - there were several "transistors" not used in this design. It would be possible to set up a trigger off one of them, and connect a cheap audio playback device (from a greeting card?) and have it trigger every time the sound stops, to re-start it, thus decreasing the overall cost even more. I'll research this. Have FUN!
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