There are two kinds of refuse which I usually make into stockpiles: useful (like bones shells etc) and useless (corpses and body parts). The useless refuse causes problems for me. For one thing, you need to designate lots of space and it generates miasma. Also, the dwarves get horrified every time they go in because they see the dead goblins. Is there a way to dump this stuff down a pit? Do I even want to? I mean can't my butchers go in and grab a corpse to butcher it? Also, do I want to have a garbage dump? I never use that except quantum stockpiles (which I don't use anymore because it's cheating). So to recap: refuse pit? , butchering corpses in the stockpile? , how does garbage really work? Thanks!
There's all sorts of ways you can get rid of stuff in DF; for example, you can crush it into oblivion using a bridge. Also, this (slightly outdated) thread suggests that you shouldn't store corpses in refuse piles, as refuse is classified to be unbutcherable - note that not anything can be butchered (e.g. Goblins).
Garbage dumps can be useful in the right place; if a child snatcher decides to make an appearance in the middle of your full barracks, you're gonna want to remove the stinking corpse. Ideally you'll want to put your refuse pile outside, as corpses that are not subterranean do not produce miasma.
Also, if you happen to be new to this wonderful game, I would highly suggest using http://dwarffortresswiki.org/ as it contains a wealth of information about several topics ranging from basic to very complex.