Run Bird Run by Ketchapp is a fun game. It is probably not one that I will keep on my device forever, but I will keep playing it until I meet all the challenges. It does have in app purchases of Candies that you can use to buy different characters, but that is about it.
Here is a video of the game to see if you want to download it. Let me know in the comments what you think.
To remove the adds it will set you back $1.99 in the app or play store, at the time of this review.