Note: I am not an Android user myself so this list is mainly based on info from friends. Recommendations and critiques are more than welcome!
- JED- A very popular dictionary app that can work off line. In addition it has kanji search by radicals, tagging, multiple language support, and so on.
- English-Japanese Dictionary (Naver)- Pretty much a carbon copy of the iPhone app of the same name. Produced by the Korean publish Naver, it requires an internet connection for most functions.
- English-Japanese Dictionary (Hironori)- A similar in both name and functionality to the Naver app listed above. I have heard that it does not play well with some Android devices, but if you are looking for a good free dictionary it is a good app to look into.
- Conjugation Japanese- An interesting app that is great for those who are still shaky on conjugating verbs, adjectives, etc. It includes dictionary files as well as drilling at various difficulty levels and even unlockable achievements.
- JA Sensei- A fairly comprehensive study app that includes everything from particles to counters to a full fledged phrase book. And its free to boot!
- JLPT Master- As the name would imply, this app will turn you into a mean, lean studying machine with drills and vocab galore. There are also paid versions tailored to each Japanese level.
- Obenkyo- Recommended by one avid reader below, this app features everything from hiragana study to JLPT-level specific kanji study as well extras such as grammar guides. It comes in both a free add-supported flavor and a paid add-free flavor.