Ok, this one may not be as cool as the venus fly trap that I spent weeks saving up for in grade school, but it takes the cake for simple genius. A wooden frame, some screen, a little bait, and it's off to the races! I came across this contraption at a horse farm in Ecuador where the flies are nearly as abundant as the wild flowers. That mountain at the bottom of the cage is the fly accumulation in one week! Thankfully, our own fly problem is not quite so pronounced in DC, but the pesky little things have still been known to ruin many a good outdoor meal, making this simple trap all the more attractive.
The bait (in this case, "dog manure", but you could use something less offensive like composting scraps) in the trap attracts flies in through the bottom, leading them up through the screen cone and into the cage. Since flies only fly up, they don't know how to escape through the cone shaped screen through which they entered. And voila!
If you are interested in building your own, Chest of Books has clear instructions.