Aedict - Excellent Japanese dictionary, also has visual kanji recognition, and one or two other handy features.
Very Easy Japanese Keyboard - exactly what it says, a Japanese keyboard. It only does hira/katakana and roman alphabets though, not kanji, so it isn't ideal. I'd love a proper Japanese IME for android, which does kanji etc, but I have yet to find one.
MX Video Player - for watching anime. It's easily the best video player I've found for android, and I've tried a few.