With all 3 of my kids, when we decided that it was time for the binkie to go, we had the binkie fairy come. We had already weaned back to only letting them have it at nap/bedtime, and we waited until they were between 2-2 1/2 so they could understand what was going on.
While my kids were sleeping, we took all of their binkies and threw them away. (We had to hunt for days before hand to make sure that we found all the ones that they had hidden around the house!) Then we put a cuddly stuffed animal that we knew they would like, and put it next to them on the bed. When they woke up in the morning we told them that the binkie fairy had come and left them the stuffed animal to cuddle with instead of using a binkie. We talked to them for a couple of weeks about the binkie fairy and what she does before we actually took away their binkies, so they understood before hand what was going to happen, they just didn't know exactly when it would happen.
We still had a few rough nights without the binkie, but overall, it wasn't too bad. They are all pre-teens now, but they still have their binkie fairy animals on a shelf in their room with the few special stuffed animals that they want to keep. I've recommended this idea to several friends and it has worked well for them too. I hope this helps! Good luck!