Apps for iPad, iPhone, Android, and on Internet
Now there is a huge resource of apps available for reading in Japanese. They are constantly coming out with new ones, so I recommend that you periodically check the Apple or Android store and do a search for 絵本(えほん)、読み聞かせ(よみきかせ)、or 読書(どくしょ).
Finding the best ones are often difficult, so I give my recommendations here.
Finding the best ones are often difficult, so I give my recommendations here.
Available for both iPhone/iPad & Android
よみキャラ

This actually is a series of apps. Each app has an animated 女子高生(joshikosei- high school girl) or 男子高生 reading a story to you. The animation is quite good and you can read along as they read to you. If you are bored with the story, you can always pause it and try "poking" the high schooler. They'll often make really funny, stereotypical remarks. Very fun and highly recommend:)
Some of the stories available are shown below:
Some of the stories available are shown below:
絵本ナビ (ehon navi)

Ehon Navi just came out with an application for iPhone, iPad, and Android that allows you to read a small collection of children's books through the application. The app is in Japanese, but it is pretty user-friendly and the illustrations/interface are quite nice.
Yomiage Ehon

This is a really wonderful bilingual "read-out-loud" app. By downloading this app, you can download 20 or so different Japanese folktale stories for free. You can change the settings so that the "subtitles" and audio are in English or Japanese. The illustrations are pretty and easy to follow along with. Below are two examples.
Princess Kaguya: from the Yomiage Ehon Series

This is a very famous folktale, also called "The Bamboo Princess." One day a bamboo cutter finds a baby girl inside a bamboo stalk . . .
Moakai'kai and the Snake God: from the Yomiage Ehon Series

Here is another book from the series above. It's about a snake god that threatens to kill a man unless he lets the snake marry his daughter.
ANN Japanese News

This is a handy app for listening to news while reading the Japanese transcript with the English translation. It highlights what is being said as you play it and you can decrease/increase the speed of the speaker's voice. It's $3.56 for Android and $5 or $6 for iPhone/iPad.
For iPad, iPhone, and iTouch
Digital Graded REaders
White Rabbit Press just came out with digital graded readers this past June (2013). The graded readers they've come out with have extended functions, such as flashcards and audio! Some titles include "Futatsu no Pan," "Kachi Kachi Yama," and "Hanasakajiisan." There are only 3 available right now, but hopefully more will come out soon. Each one costs $3.99.
https://itunes.apple.com/us/app/kachikachiyama/id654676226
https://itunes.apple.com/us/app/kachikachiyama/id654676226
おとえほん (Read aloud books)

There are many type of "ehon" available in the Apple store. I thought this one was nice because it reads at a comfortable pace with really relaxing music in the background. This one also belongs to a series of different apps, each with a different story. Most of the stories are 昔話(mukashi banashi).
おしりたんてい (the butt detective)

This is an interactive childrens book. It's really silly, but very cute!
漫画の新聞 (Manga no Shimbun)

This is a fun app for reading about Japanese news and pop culture in manga format. The only downside is has a lot of kanji without furigana, so sometimes its hard to understand. However, the graphics are really nice.
You can also read this online at
http://newsmanga.net/
You can also read this online at
http://newsmanga.net/