With my sister, my folks chose not to use a pacifier, and she learned to suck her fingers instead,and sucked them (at least while sleeping) till she was WAY too big a girl to still have the habit (like dentists were worried about her harming her permanent teeth).
With my brother, my folks used pacifiers, so it was much easier to stop the sucking habit.
You can take away the pacifiers completely when they get too old to for them to be appropriate. You can't take away thumbs and fingers. If you throw out all the pacifiers, there's no way for the little one to sneak them. There's no feasible way to keep them from sneaking a thumb into their mouth.
But I don't have kids, so feel free to take my input as lightly as possible.
