My automatic garbage disposal. Throw items into the chest and hit the button for magic :3 It's not much to look at, so I'll post a cut-away view from when I was testing it in SP.
This is the station trigger. When the minecart chest comes into to the station, it stops over a piece of powered rail, which is always on, with a hopper under it. The items start passing from the chest into a hopper. Whenever a hopper has items passing through it, it gives off a redstone signal through a comparator which in turn negates a signal to the powered rail, turning it off. Once the chest is empty, the hopper no longer gives off power, re-inverting the signal to it's normal state. This turns the power back on, and the minecart is sent back to it's home.
The hopper is connected to a dropper which has lava under it. A dropper also gives off a redstone signal through a comparator if it has items. Here, the signal loops back to the dropper causing it to instantly drop any item entering from the hopper.
At the end of the cycle, the minecart is back where it started and you are garbage free