imiwa? is an English-Japanese/Japanese-English dictioanry using JMDict files based on Jim Breen's EDICT project. Free.
Eijiro on the WEB (iOS)
This app queries the Eijiro 英辞郎 dictionary on the web to search for English and Japanese words. Free.
Android Free Offline Dictionaries
Japanese Text Analyzer (Android)
This is a morphological analysis tool for Japanese language, providing linguistic information, proofreading aid, dependency analysis, ruby glossing, kana to kanji conversion, and WWWJDIC lookup. Free.
Jisho is Free, Convenient, and Easy to use for finding English, Japanese, and Romaji word variations.
POPjisyo is a free Japanese English translator that can pick out and provide information on individual words and phrases.
Kōjien Dai-roku-ban 広辞苑 第六版 (Android $)
Kōjien is the gold standard of Japanese-Japanese dictionaries, and this version includes color images. Does not require an internet connection.
Daijisen 大辞泉 (Android, iOS FREE and $)
A comprehensive Japanese-Japanese dictionary including some images.
Daijirin 大辞林 (Android, iOS $)
A comprehensive Japanese-Japanese dictionary, including images for some entries, and facilitates sharing words via Twitter. It includes a jump function, handwriting recognition, and browsing.
Iwanami Kokugo Jiten Dai-nana-ban Shinpan 岩波 国語辞典 第七版 新版 (Android, iOS $)
Iwanami's Kokugo Jiten 7th Edition, similar in interface to Daijirin. It includes browsing capability and handwriting recognition. No internet connection required.
Meikyō Kokugo Jiten Dai-ni-han (Android, iOS $)
It supports handwriting recognition, and includes a kanji dictionary and several appendices containing information about topics such as lunar cycles.
All国語辞書, Japanese ⇔ Japanese (Android, iOS)
This dictionary searches across a variety of online 国語辞典, including Yahoo!, Weblio, Goo, Excite, Kotobank, Google, and more. It supports handwriting recognition for kanji and kana on Android. Free.
Weblio 辞書 (Android)
Weblio 辞書 searchces Weblio's site for encyclopedia and dictionary entries. Free.