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>https://play.google.com/store/apps/details?id=com.alexisblaze.japanese_grammar

Port of Guide to Japanese by Tae Kim. Includes bookmarks, day/night modes, easy navigation and clickable translations.

 

https://play.google.com/store/apps/details?id=com.google.android.inputmethod.japanese

Official Japanese keyboard.

 

https://play.google.com/store/apps/details?id=com.jb.gokeyboard.langpack.ja

For GO keyboard.

 

https://play.google.com/store/apps/details?id=com.sage.ljp

Offers tests to help you improve your Japanese, including Kana stroke order and pronunciation.

 

Dictionaries:

https://play.google.com/store/apps/details?id=com.umibouzu.jed

 

https://play.google.com/store/apps/details?id=com.space.japanese

 

https://play.google.com/store/apps/details?id=ric.Jsho

 

[Android] Jade Reader

https://play.google.com/store/apps/details?id=com.zyz.mobile&hl=en

Free open source text reader. Provides instant offline EDICT lookup. Also allows you to conveniently save words  from the text you're reading into a list so can add them to Anki later.

 

[Android] OCR Manga Reader for Android

http://sourceforge.net/projects/ocrmangareaderforandroid/

Free and open source Android app that allows you to quickly OCR and lookup Japanese words in real-time. It does not have ads and does not require network permissions. Supports both EDICT and EPWING dictionaries.

 

[iPad/iPhone] Wakaru

https://itunes.apple.com/us/app/wakaru-learn-japanese-by-reading/id351047145?mt=8

Pretty much same as Android's Jade Reader. The free version will annoy you with a suggestion to purchase the app while looking up the word every now and then. Costs $6 for the app. Costs some more for pdf support.