KanaWeb is a "Rikaichan for iOS" that provides readings and definitions of highlighted words, in its own web browser. Free, available for iPhone and iPad.
Jade Reader (Android)
Jade Reader provides readings and definitions of highlighted words in text files, similar to Rikaichan. It can directly connect to Aozora Bunko. Free.
Kanji Kentei 漢字検定 (iOS)
An app to practice for the Kanji Kentei exam; all levels included. Paid.
Conjugation Japanese (Android)
A quiz that randomly asks you to conjugate various verbs. No way to search for a specific verb's conjugation; it's a quiz only. Free.
Flashcards* is a flashcard app for both iPhone and iPad, which allows users to create their own cards. Users can also insert images and download card decks. The app is free but ads can be removed for a fee.
AnkiDroid lets you create flashcards in the app or on your computer using Anki, and you can then transfer them to your mobile device. Over 6000 already created decks are available and it also syncs with AnkiWeb. Free.
Flashcards Helper (Android)
Flashcards Helper allows users to create their own cards, and is able to sync and share cards. Users can create cards on their computer and sync with the app. Free.
iFlash Touch (iOS)
iFlash is the counterpart to the Mac OS X application iFlash, and allows users to sync decks of flashcards from their computer to their iPhone, and back again, over a wireless LAN. Free.
StickyStudy: Japanese + Dictionary (JLPT Vocabulary & Kanji Flashcards) (iOS)
StickyStudy provides cards to study for the Japanese Language Proficiency Test (JLPT) along with kanji by school grade. It is a paid app for iPhone and iPad.
Anki Aniki (Android)
Flashcards for the JLPT N1 - N5, kanji only. Free with a paid non-ad version.
Japanese Vocabulary (Android)
Japanese Vocabulary provides flashcards for the old JLPT levels 1-4. Its English translations of example sentences are poor, but the translations for the individual words are solid. Free.