This may seem like a crazy idea, and it may only work with an older child...but it actually worked for us! My son was intensly attached to his binky until well after he was 2 years old. It was driving us crazy and we were soooo tired of looking for the darn thing everytime he lost it. So one day, we used an idea from SuperNanny. One night before bed, we told Devon that the "binky fairy" was going to come tonight. She was going to take his binky and give it to "a nice little baby who needed it." We got out a brown sandwich bag and he decorated it with crayons and stickers. We then wrote a note together that said, "Dear Binky Fairy, please take this binky and give it to a nice little baby who needs it." We then went out onto the porch and he set it down, and we again reminded him that the binky fairy was going to come and take it that night, but maybe she would leave a special treat for him.
That night, he went to bed with no problem, and no binky! We could NOT believe that it worked! LOL. The next morning, he was delighted to find the sandwich bag filled with a few little toys and his favorite snack. He never asked for his binky again :)