Sago Mini Superhero ($2.99, iOS, Amazon, Google Play, Windows)--Where will Super Jack the Rabbit go next? How will his story unfold? Great app for preschoolers, but loved even by older kids for the humor hidden around each corner.
Cookie Next Door-Rainy Days (FREE, iOS only)--A graphic novel that allows you to record your voice to add the words that tell this (currently wordless) sea-faring tale. There's also a sequel--Rainy Days 2. I am amazed that this one is free!
Loose Strands (free preview / $4.99 full, iOS, Google Play, Amazon)--Wacky choose-your-own-adventure story, complete with a story map that shows you where you've been and what avenues have been cut off as you make your choices. Not a great choice if you are icked out by hair.
Toca Blocks ($3.99, iOS, Google Play)--Often compared to Minecraft, Toca Blocks allows users to create their own world, building with blocks that have different properties. Mix multiple blocks together to discover new blocks!
Infiniscroll ($1.99, iOS only)--A story-creation tool like no other!
Mr. Glue Stories (FREE, iOS only)--A set of e-books with a few choices for the user to allow for a custom-made story full of silliness. Also includes some options for adding your own color enhancements to some of the illustrations and record your own voice for some of the sound effects.
Toontastic (FREE, iOS only)--Create your own animated cartoon and record your voice as narrator. Tons of options to choose from and a great guide through the various points of a storyline from set-up through resolution. Lots of great music options built right into the app.
Telestory (FREE, iOS only)--by the same company as Toontastic, this app allows you to record your own "television show"--complete with virtual costumes, action-prompting cards, music and sound effects.