My daughter was 3.5 when we went to the dentist and he said her teeth are not growing together in front because of her pacifier. If she didn't quick now, her bones may have formed around her crooked teeth and she would need braces! She only uses it to sleep at night (for comfort, I sucked my thumb for comfort until the age of 22...I really needed it...and I didn't want to take that comfort from her..but my teeth were fine). So we made the decision to quit, I thought her beautiful smile was more important.
So I made the hard decision to take her binky completely away from her. I sat down with her at night, put the binky in a "magical place" that the binky fairy could get to (not in her bedroom, but outsinde, and she's always wanted to sleep with the windows closed for fear the binky fairy would come and take her binky's when she's sleeping), with the promise that she could go to the toy store the next day and get any gift she wanted (within reason).
I told her what the dentist had told her earlier, that because her teeth were growing crooked, she couldn't have binkies anymore. She was ok with that. She went to sleep in our bed watching TV with me (so she didn't need her pacifier), and I moved her to her own bed once she was asleep. She woke up in the morning with a smile on her face (I think I was more traumatized than she was!). We went to the store and she got a doll.
The next night wasn't so easy. She went to bed just fine (in her own bed) but woke up for her binky at about 4:00A.M. and cried for an hour! I just held her and told her I loved her. My husband came in and told me to give her one, but she had been crying for an hour already and I didn't want all that crying to be in vein. After she fell asleep again, she was fine and hasn't cried since. Yahoo!
We have found binkies lying around that house, and we just say, "That darned binky fairy...she forgot another one!" We give each other a wink and a smile and go put it on the magic spot for her to take it that night.
I have to admit, the entire process was much worse for me than her, I was really surprised. Do it now before she gets old enough to really remember giving it up (like my step-daughter, she still feels sad and she had to give hers up when she went into kindergarten).
Oh, and my daughter has never been a thumb sucker, and still isn't today.