I think there's some confusion over how these buttons work.. please allow me to explain.
Pass: Takes you out of the running for the item entirely
Greed: Rolls for the item if nobody pushes Need
Need: Rolls for the item and overrides Greed rolls.
So let me summarize.. if you push Need on an item, you only roll against other people who also pushed Need. As soon as anyone Needs on an item, Greed rolls are automatically discarded. The only time Greed ever comes into play is if nobody pushes Need.
Essentially, you should always Greed on items you can't use and Need on any items you need. Once you're a Sergent Second Class with your GC, you can turn in pink and green-quality items you don't need for seals.
Someone rolling Greed does not affect your Need roll in the slightest.
Now, if you've got someone in there competing with you for gear legitimately, you can ask them to pass on something you're looking for. And it's entirely up to them whether they do that or not.
EDIT because this wasn't here:
It does, but when someone then Greed's on something it holds the item in the queue for longer than if you just simply passed the item.
Items will roll as soon as everyone has made a selection. If something is sitting in the loot pool collecting dust, it's because it's waiting for someone to push SOMETHING, ANYTHING. Edited, Sep 9th 2013 11:42am by Callinon