I'm a strong advocate of garbage chutes with atom smashers at the bottom of the chute. Place several of them around your fortress, link them all to a single lever or repeater, zone them all as garbage zones, and your dwarves will dump the garbage in the nearest chute. While you could use a repeater, I just assign a dwarf to do it. I remove all of his other skills except for healthcare, assign him the custom title "Atom Smasher" and make it so that only he can use the lever. His job, for the rest of eternity, is pulling that lever. Maybe sometimes also tending to a patient. But mostly pulling the lever.
Hmm... Interesting, and I might just use that as my permanent garbage disposal solution next game. Personally, I'm afraid of accidentally having something tossed in the garbage I might one day want (typically, goblinite, although there's always more where that came from), so I don't set it to automatic, and instead have an airlock system to get to the switch so that no moron tries to dump garbage while the atom smasher is in operation.
A "chute" doesn't seem terribly appealing to me, as I tend to build vertically, anyway, and I save maybe 10 steps to the nearest dump.
I COULD, however, theoretically use a water flushing system to push items horizontally towards a main garbage chute... but unfortunately, many items (most notably stones) do not generally get pushed by water due to their mass and density, at least as far as 16d was concerned.
I also made my last atom smasher out of bismuth, just for that neat magenta color...