One of my favorite app designers are the folks at Tiny Hands. They have a suite (but you can buy apps separately and get free mini trials) of apps for the 2-5 set that are progressive in challenge but consistently high in fun.
Since I am always looking for positive (read: active) tablet use, I like the way these apps require matching, categorization, counting or visual-percpetual skills to be rewarded at the end with a cute character suspended on pop-able balloons. The graphics are very simple, and an over-excited toddler cannot tap themselves through. They have to think. Themes reflect topics that toddlers can recognize and nothing controversial. There are no warring ninjas or exploding bombs. But there are plenty of animals, vehicles, and even some music. Levels of play are indicated, but the child is not restricted from trying higher levels.
As an occupational therapist, I love using the app crayon or the app stylus for these games. The drag-and-drop function builds hand strength and control without a child realizing that they are doing so. It is just so much fun.
Tiny hands gets tiny minds working too!