This is a pretty common consumer product: a device approximately the size of a votive or maybe a tealight that behaves basically like a candle, in that it has a small LED that flickers and fades. The reason I want to make one rather than just buying it is that I have a special need- to be able to turn it on and off without contacting it. A few years ago I made some balsa and paper lanterns that can be hung from the ceiling on a string. A tealight in the bottom provides nice light, and the dozen or so that I made create a very warm atmosphere in a room where they are the sole illumination.
Of course, lighting all those candles is no fun. It requires hauling a chair around the room, getting up and down, and trying not to catch the paper on fire. Putting them out is similarly taxing, unless you let them burn down over four to five hours. Obviously an application ripe for electronify-ing, but an electronic light has the same problem: to turn it on, you need to get up on a chair, pull the light out of the lantern, turn it on, and drop it back in. I know, not SUCH a huge deal, but still more than one wants to do regularly.
So, my solution is a pretty simple one: make the lights magnetically switched. It's pretty simple to do- just put a reed relay in the system and drive the thing with a PIC. The PIC stays in sleep mode until you activate the relay, then it flickers the LED until you activate the reed relay again. Activation of the reed relay just requires waving a magnet on a stick near the lantern. A PIC in sleep mode can sit in a circuit with a couple of AA batteries for months without draining them.