So, as I mentioned, I recently actually got a smart phone. So, with it there was a variety of apps to try and play with, and yes, there are a number of apps based on Oz in some form. Here's the first two I tried and enjoyed. (I also tried a couple apps called "The Complete Oz Vol. 1" and "The Complete Oz Vol. 2" which were the Baum books in an ebook format. However, I find accessing Project Gutenberg much more worthwhile, particularly as the pages appear to be static and I couldn't read the tiny type on my phone. Maybe if I had a tablet or a bigger phone, it would be worth it. They were free.)
Please note that these particular apps are for the Android platform and were used on a phone running version 4.1: Jellybean. They are available on the Google Play store. They also seem to be available on Apple products.
The Wizard of Oz by Boluga is an abridgement of Baum's first Oz book as an interactive picture book using Denslow's original illustrations. Some are simply animated (Dorothy melting the Wicked Witch) while a good many others let the user actually interact with the illustrations. Set the Scarecrow free, oil the Tin Woodman, and even fill the poppy field with more poppies!
I thought the interactive pages were fun, and they can be reset with an icon in the corner, but there seemed to be too few. Still, for only 99 cents, you can't complain too much.
Temple Run: Oz is the only digital game released for Oz the Great and Powerful. (Sometime I should tell you about the only Return to Oz video game.) It's a variant of the Temple Run game series, in which a player runs through a course, jumping over obstacles, sliding under them, running to the side of them, or making a very sharp turn.
Jumping is done by swiping your finger (or a stylus) on your screen up, sliding is done by swiping down, turning is done by swiping to the side you want to run to. Going to the side is done by tilting your device to the side.
By default, you control Oscar from the film, running without his coat or hat down the yellow brick road, pursued by the winged baboons. You have to stay one step ahead of them, so they don't catch you and carry you off to who knows where! But on the other hand, don't run into a rock or tree root or fall into a ditch because that would be quite... counterproductive. Also, there are plants that will try to snatch at you that you can run by, but running through them will slow you down and possibly let you get caught by a baboon. Along the way, you can pick up coins or (very rarely) a gem.
The game costs 99 cents to get, but the reason why it's so cheap is that you can buy more coins or gems (which will let you continue if you tap the screen quickly if you fail). The coins will let you purchase costume changes for Oscar adding a hat, or letting you run as "The Great Oz" (Oscar's stage persona at the beginning of the movie). Also, you can purchase an alternate character and run as China Girl instead. You can go ahead and spend more money to get coins to purchase these, or just keep playing the game and slowly build up your coins.
The game is actually pretty fun and the challenge actually makes for a lot of repeat playings. In addition, you can upgrade the game by downloading (for free) additional stages you can run to. I'm not sure if you unlock these when you get there, but the other stages are the Dark Forest, the Emerald City, and the Winkie Country.