In my 37 years in pediatric dentistry, I have seen all sorts of responses from parents who have a child that sucks a thumb or finger. Everything from "it's no big deal", "it comforts them and helps them get to sleep", to "how can we stop it now?" When I get asked about it and what to do, I always have a definite answer, "it depends!"
Here are some things I consider when counseling a parent on thumb sucking:
1) How old is your child? I don't get too worried about it until they're in the 4-6 year old range. If they are younger than that, and it helps them get to sleep, then don't worry about it. If they are older, then I should take a look.
2) How often do they suck? Is it all day or just at night? Is the finger or thumb just sitting in their mouth or are they actively sucking? Just at night isn't as bad as all day long. And, "passive" sucking is less damaging then "active" sucking. If they actively suck all day long, then I should take a look.
3) Is the habit affecting their teeth and will they need braces later? Again, some habits do not affect the occlusion and so I don't worry about that. But if their upper teeth are starting to stick out then I should examine them. Most children, if they stop before the permanent teeth come in, and the dental arches have not been affected by sucking, should have no long term problems.
4) Has the parent tried to stop the habit? What have they tried? At ages 4-6 I recommend trying the prize or reward approach. If that doesn't work, then you could go to the mitten at night or something else to remind them when the finger goes in the mouth. If that doesn't work and they are still actively sucking at age 5, then I should see them.
5) The main thing I suggest is not to make this a power struggle. It should be "matter of fact" and if I am needed to intervene with some sort of reminder appliance, it is not a punishment but just something to help them be aware when their thumb goes in their mouth. The child needs to "buy in" to this. When we do place an appliance, I usually leave it 6 months, and have never had a child go back to sucking after that.