I just came across NIGHTY NIGHT, the app, and it is so, so wonderful. I play with it before I go to sleep, after I've put the kids to bed! (Yeah, okay, I may be taking it too far but I love it!) It's not a story, really, but it feels a bit like one in the sense that there is a narrator and all the animals go to sleep, one by one.
I highly recommend it if you have little ones. The other apps by the same company (Fox & Sheep) are great too - especially PETTING ZOO, for anyone with an artistic bent. Honestly, PETTING ZOO feels like one of those groundbreaking wonderful pieces of work that will become a classic in the future. If there will ever be such a thing as a 'classic app' in the future!!
But back to NIGHTY NIGHT. If you do get it, do change the setting to 'snowflakes' when it gets close to Christmas. It's so Christmassy! And it's worth investing the 99cents or pence to get the three extra animals too. I just love it so much. Ahem, as you can probably tell.
PS Other story-like apps for kids I've loved are anything by Nosy Crow (Cinderella, for example, is pure joy); anything by Storybots (the fairytale book is just genius – the cameo roles by various fairytale characters is wonderful). There are probably others...