Thumb and other finger sucking habits usually have the effect of pushing out on the upper teeth and pushing back on the lower teeth. As the upper teeth move forward, spaces develop. As the lower teeth move inward, crowding occurs. These people also usually have "anterior open bites." This means that when the person closes his or her mouth all the way, the front teeth don't meet since the thumb or finger has prevented them from erupting. Depending on the aggressiveness of the habit, we usually see a width mismatch between the upper and lower arches. Typically, if the child is aggressively sucking her thumb, this constricts the cheeks which in turn constricts the upper arch form. Normally, the upper back teeth are supposed to be wider than the lower back teeth. With aggressive thumb suckers, the upper back teeth can be inside the lower back teeth (when the upper teeth are inside the lower teeth this is called a "crossbite").
Parents may also wish to consider other aids: