Some of you may remember, as I do, a time when there was no Greed button, only a dice and pass options on looting. Either you wanted the item, or you didn't. Or, it was BoP loot, in which case, as I remember, everyone was supposed to pass, and then you all decided what to do-- though it was so long ago, I can't quite remember why that was...
At any rate, that time is over, and now we have the option to Need or Greed roll on loot that shows up, so it's pretty clear what to do when loot drops-- if you need it, roll Need, and compete with other Needers. If you just want, roll Greed or pass, and everybody's happy.
Except, as with everything, there are exceptions. Nesp from Lightning Blade brings up one of the most common-- he's a jewelcrafter, and he's wondering if he should roll Need or Greed on gems-- sometimes, he's the only one in the party that can cut them, but then again, anyone can use them after they're cut. Likewise, I think there's a little confusion about things like Fel Armaments and Arcane Tomes as well-- yes, people of the opposite faction from Aldor or Scryer shouldn't roll on rewards they don't need, but should the right factioned people all roll Need or Greed? Likewise, everyone needed things like Corrupter's Scourgestones-- should everyone in that case roll Need, or just roll Greed?
As Blizzard says (sensibly) in the thread, the best policy is to actually decide on a policy within the party before you have to-- nothing worse than losing an item to someone who can't use it, or taking an item accidentally that you don't really need. My plan is probably the default most players use: if you need it (as in, you can wear it or turn it in ASAP), roll need. If you don't (or you're going to sell it at the AH or DE or vendor it away), roll greed, and live with the consequences (there's always more loot to gain). But whatever works for you is what works best.