Common Sense Media has a list of recommended apps for kids of all ages. Check out the list for both free and paid apps organized by age and mobile device. You can also print out the guide if you'd like.
Check it out here: http://www.commonsensemedia.org/guide/best-first-kids-apps
Check it out here: http://www.commonsensemedia.org/guide/best-first-kids-apps