Thumb and finger sucking.

The sucking reflex is normal and healthy in babies. However, a thumb or finger sucking habit can cause problems with the growth of the mouth and jaw, and position of teeth, if it continues after permanent teeth have erupted, between four and seven years of age.

Thumb Sucking and Teeth

Despite popular belief, young children who obsessively suck their thumbs will generally not develop dental problems due to the thumb sucking. However, if they continue to suck their thumbs when their second teeth start growing in, there’s a risk for developing dental abnormalities.

Thumb Sucking

It’s very normal for older babies to suck their thumbs. In fact, this practice is considered normal until children reach 2 1/2 years.
From: YeahBaby.com