If you’re going to go Android for Japanese first you need a keyboard. I like Simeji. It’s ugly, but very useful… and really, the only good choice out there, to be honest:
https://market.android.com/details?id=com.adamrocker.android.input.simeji
Also, if you like to add Japanese-style emoticons, then Kaomoji List is a great add-on to Simeji. It’s activated through the “mushroom button” on Simeji’s keyboard:
https://market.android.com/details?id=com.zeroindex.mushroom.kaomojilist
If you want to draw kanji by hand, then I recommend HanWriting IME:
https://market.android.com/details?id=com.KwanLye.android.HanWriting
For a dictionary, there are a couple of options. My preference is DroidWing. It works great with EPWING dictionaries (just create an EPWING directory on your SDCard) and with web searches, if you know what search strings to use. You can search multiple dictionaries all at once, which is powerful.:
https://market.android.com/details?id=com.aokabi.android.droidwingfree
If you just want EDICT, then it’s hard to beat Aedict. It’s free:
https://market.android.com/details?id=sk.baka.aedict
Vertical Text Viewer is great for reading é’空文庫 (aozora bunko) formatted books. é’空文庫 is the Japanese version of Project Gutenberg, only the difference here is that the format they use has become an “underground” standard of a sort. You can even buy books, have them sent to a professional to be scanned professionally, and then format them yourself in é’空文庫 format. (The books get destroyed in the process, though.) Of all of the é’空文庫 readers out there, I like Vertical Text Viewer the most. It has a Mincho font you can download inside the app for extra legibility, and when you press and hold on a word, you can send the word to DroidWing to look it up! VERY handy.
https://market.android.com/details?id=org.example.android.npn2SC1815J.VerticalTextViewer
If you’re learning Japanese, chances are, you’re also struggling with a way to remember everything. I hope you’re using an SRS. My favorite SRS is Anki, and there’s a port of Anki for Android, called Ankidroid.
https://market.android.com/details?id=com.ichi2.anki
When you’re in Japan, post offices are really useful places for doing 2 things: sending crap home, and getting money for cheap. Finding them, on the other hand, can be tricky. This app claims to do it. (Requires a connection.):
https://market.android.com/details?id=jp.co.efficient.pnpostoffice
This last app is just cool: the Hyperdia search app– you can use the Hyperdia service to search for ways to get from A駅 to B駅 (A Station to B Station) all over Japan. Of course, these days, that might not work exactly as you think. Also, this requires an online connection to work:
https://market.android.com/details?id=com.hyperdia.android.activity