What I do with my crier is call her bluff so to speak. I treat the crying the same as if she was yelling and having a tantrum because to a certain extent that is what she is doing. tears get sympathy tantrums get timeout. Well when you are three and use tears as a way to manipulate just as you would if you were having a tantrum and screaming and stamping your feet you get treated the same.
When you start to look at the crying from that perspective it makes dealing with it easier in the sense of negative consequences do work eventually. Now I am getting to the point I can just give her "that look" and she turns the tears to a pout/blubber but at least it is quieter.
We are so conditioned to respond to tears that we forget that kids use them instead of words and instead of actions when they are older because they learned in infancy/toddlerhood that the method worked. Now they are three and time to teach a new lesson - they don't work.