Edited to represent latest research.
You may want to check out http://dwarffortresswiki.org/index.php/User:Vasiln/Undump
for pretty diagrams that are probably easier to read, as well as a design variant that's more reliable, at the expense of greater complexity.
h is hatch over channel, b is bridge over channel, ^ is pressure plate (citizens trigger) linked to hatch and bridge, # is wall, s is a single stockpile that spans over the hatch and is set to take from stockpile t
. is floor (or whatever), t is stockpile with same settings as s, created after stockpile s
Orientation and build order may or may not matter
To spell it out, stockpile generates a "bring item" job, but when the dwarf tries to bring an item to the right-most stockpile job, he finds no path, and drops his item. Luckily, he's already standing on a stockpile (with the same settings) when he drops the item, so he doesn't keep on trying to move that item.
What it functions as is a sort of quantum stockpile, but with normal stockpile sorting, without having to designate anything or reclaim anything, and you can still use the "dump" function to drop things in the magma. This isn't just nice for reasons of space and automation-- since this stockpile is never full, it also means that if there is an item on the map that can be put in this stockpile, and your dwarves can path, it WILL be stockpiled.
Doesn't always play nice with other stockpiles, since it can hold infinite goods, but "take from" settings work fine.
Works slowly. Consider expanding stockpile t for a sufficiently sized reserve in cases of high throughput (raw materials, etc).
An earlier iteration saw very slow dwarves occasionally making it to the last stockpile square, thus breaking the undump; the addition of the bridge doubles the length of time that the lure tile is inaccessible. Haven't seen any problems since I started using the bridge. EDIT: Stuff still makes it to the lure. See the wiki page linked above for a different version that's functioning perfectly so far.
It's not uncommon for dwarves to drop goods on the pressure plate instead of the stockpile; that's one of the reasons there's the feeder stockpile, which will prevent infinite loops that could otherwise occur. In my experience, about 1/3 of the goods make it to the pressure plate, and 2/3 to the stockpile, but this probably depends on the dwarves and the items in question.
If your dwarves are both drawing from and delivering to the undump, dwarves will occasionally drop an item on the way to the stockpile. So don't use it for food (or anything else that will rot off of a stockpile.)
I think there are a huge number of applications:
1) Zero workshop clutter: Since any number of things can be stored on the tile, you can put your masons to work making doors nonstop and never have to worry about the size of your door stockpile. Brewer's are another on of those shops that always give me trouble. EDIT: Use with caution for stills. Use of bins or barrels can lead to hauling loops.
2) Raw material: This can put a stockpile a single tile from a workshop-- a sorted stockpile, that you don't need to manage. They're small enough that you can easily have separate stockpiles for individual raw materials, blocked off however you'd like.
3) Mini Mass Pit: Only ever need a single hatch for your mass pit. Requires diagonal redesign, with an untriggered hatch east or west of the southern s stockpile tile, but that shouldn't break functionality. Don't have to worry about empty cages with this plan, but you can always build one for the empty cages if that's what you want.
4) Socks: Dear God, socks. Never again fear that an unowned sock is exposed to the wind and the rain.
5) Trade goods: No more bins necessary. All goods you'll ever want to trade, right next to the depot.
6) Refuse: Tiny design means you don't have to worry about it getting cluttered up with goblin corpses, and it's easy to leave a single tile open to air. If you don't care about getting any bones out of them, it can be designed to be magma-floodable. EDIT: Refuse attracts vermin; vermin attracts cats. Cats don't trigger pressure plates, and they kill vermin and can leave the vermin on inaccessible stockpile squares. Use with caution.
7) Mandated goods: Mayor like quivers, and now you have 500 of them-- can't even run a designate dump on your front porch to clear the goblins because of prohibition of exporting quivers? Here's how you store those goods, and whenever the mayor drops his export mandate, they're all in a nice single square, ready for designate-dump.
1) Food. It won't always make it to the stockpile square, and will rot.
2) Drinks. They don't rot, but to stockpile them, you need to enable barrels, and that has the potential to lead to an endless loop of pick the barrel up, drop the barrel.
I'm also playing with a dropping version of this-- instead of the near stockpile square, I have another hatch, combined with a one-way, goblin-grinder style path to the undump that automatically drops goods on the way out. So far, this is working without a hitch (I've got it dropping skulls into magma), but there's the theoretical potential for dropping a dwarf rather than his goods when doing this. So far, it hasn't happened, so I imagine the risk is slight. (You can make a foolproof dropping undump, but it's incredibly complicated and runs really, really slow.)
EDIT: Just a warning, because people seem really excited about this-- while I've tested this, it's not always been in a real-fortress environment. I've been testing using super-fast dwarves (EDIT: slow dwarf test later in thread), and maybe that affects things. Even then, there's an occasional problem, and I don't know exactly how many headaches this would cause vs. how many headaches it would resolve. So I'm looking forward to anybody's real-fortress reports of the design-- there's always room for it to not function as well as intended. EDIT2: I've edited this post as I've performed further testing, and I believe that the design given above, within the limits specified, is functional and useful. Some of this thread is in reference to previous designs that aren't as useful. Last tested, v34.02.