Quote From: amymashleyOK ,  
We have a 3 month old boy, Charles. He started sucking his thumb about a week ago only when he is tired or sleeping. Chip and I both dont want him to get use to doing that . Chip had a bad habit when he was younger as he was told by his mother that he sucked his thumb and it was really bad stopping it. For me , when I was younger I sucked a pasifier, and also a bad thing to get into doing. 
What should we do? We keep pulling the thumb out. But the little thumb goes right back in the mouth... One person told us.... Put a pasifier in place of the thumb if he will take it. CAUSE 
It is easier to throw of the pasifier away BUT you cant get rid of the thumb. What do you think? 
When my son was little we gave him a pacifier to suck on. Neither my husband nor I liked the idea of a three year old trying to talk around the stupid thing. So, what we did was let him have the "binky" whenever he wanted it until he was one year old. On his first birthday we took all the things out of his room, diaper bag, and where ever they were around the house, and made them "dissappear". That night after he went to bed, I took them out to our garage and put them with all his other clothes and things that he had outgrown.
Yes, he fussed for a couple of days, and my husband and I wished that we still were using the dumb things, but agter a week, my son had forgotten all about ever having them. Several months later he found one that had been in the couch cushions and went and threw it into the trash. He didn't even hesitate or try and put it in his mouth.