My twin boys are 21 months old and are very attached to their binkies too... only for nap/bed time mostly. I plan on letting them let it go in their own time. I did the same w/ my daughter, she just one day woke up and was ready to give it up on her own at about 2 y/o. Their Dr. scolds me on it so I don't mention it at checkups anymore lol.
We used to place the pacifiers at the same spot every day. My kids would ask for it and we handed it to them. One day, my daughter asked for it and I told her it wasn't there. It was "gone" (we just put it somewhere else) and she never asked for it again. She was probably 18 months at the time. My son though, it's a different story. If it was up to him, he'd still have it. He's 2 and a half, mind you. His last pacifier broke and we never replaced it so now, he sucks his thumb all the time. So, the best advice I have on this topic is, whatever you decide to do, go gradually. He just might find himself something else to suck on (thumb, blanket, toy, etc) and it may not be much better than a pacifier.
I have heard the cutting method works well. You keep cutting a little bit of the rubber off bit by bit each day until nothing is left for them to suck on. Also there are books and kits you can use to send the binky off to the binky fairy and such....
My boys are 19 months, and one of them still uses his binky to sleep with. The other just gave it up at about 5 months. Their Dr. said that it isn't something to be concerned with at this age and that sometimes if they are really attached to it and you take it away before they are 2, they could start sucking their thumb. I would just give it time. I took my sons binky away during the day cold turkey and that worked well, but neither one of us is ready to give it up at night.