Who remembers color by number? I loved them. Such a simple idea and yet it can help kids work on several things (while creating artwork for the refrigerator)!
The coloring itself will work on hand strength and endurance especially when they have to color the larger areas. It will also allow you to work on grasp patterns (if you break the crayon into smaller pieces it will encourage a tripod grasp). Visual motor skills are used by working on having the child stay in the lines. For kids that are just learning you may need to build up the lines or use raised lines so they get increased feedback. Along these same lines, the child can work on scanning to see where the numbers are for each color. If you want to work on letters you can make your own picture and use letters instead of numbers. It also helps with following instructions because there is a set color/number correspondence.
You could also print out a blank picture and have the child try to create their own and see what colors they would put in each area. It allows them to plan out the picture ahead of time.
How have you used Color By Numbers?