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 English Dictionary & Translator Box / 英語日本語辞書 (iOS)
This is a multilingual dictionary, geared toward Japanese and English (but with many more dictionaries to install), that searches multiple dictionaries for results. Free.
MultiDict searches Naver, Goo, and Weblio for English and Japanese words. Free.
Webdict searches several online dictionaries, including Eijiro, Wikipedia, and LONGMAN. Free.
Japanese Verbs (Android)
This app provides a verb conjugation dictionary (including polite and plain forms) as well as quizzes. You can search in either Japanese or romaji.
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.
Ultra Sōgō Jisho 2013 ウルトラ統合辞書2013 (Android $)
This app contains a variety of dictionaries and encyclopedias, including full color images, such as 広辞苑, several Japanese-English and other European language dictionaries, 新漢語林MX, 角川類語新辞典, a contemporary usage dictionary, and more.
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.
Sanseidō Kokugo Jiten 三省堂国語辞典 (Android, iOS)
Sanseidō's Kokugo Jiten is available as both an Android and iOS (iPhone and iPad) app. It does not include images, but allows for browsing and highlights search terms within words. Paid.
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.
This searches Goo's site for 国語辞典 entries on various topics. It simply displays information from Goo's site and does not support handwriting recognition. Free.
Weblio 辞書 (Android)
Weblio 辞書 searchces Weblio's site for encyclopedia and dictionary entries. Free.