One app that has lived on my home screen since it was released in 2008 is very simply called Japanese.
I've tried dozens of other Japanese dictionaries and language apps, but I always ditch them after a few uses. Japanese, by renzo Inc., is exceptional. I tell every single person who expresses any interest in learning Japanese, regardless of whether they're a beginner or advanced, to get this app.
When I was studying Japanese at the university, I carried around a thick, heavy book by Nelson that was a required tool of all Japanese majors, the Japanese-English Character Dictionary. I still recommend getting this book if you're serious about learning Japanese. One of the best things I learned early on was how to look up any Japanese kanji character by its radicals. The 214 historical radicals are the building blocks of every Japanese kanji. Think of them as the elements that, when combined, create the thousands of different kanji characters available. You learn to look up characters by 12 steps. The first, for example, is the total stroke count of the radical.
Academically, this is awesome, and useful as you learn how to read. But it's not so practical when you're out and about and just need to know something right away. Or if you're out at an Izakaya having drinks with friends. Not cool to pull out the big, heavy book.
That's where Japanese comes in.
It has 170,000 entries and over 70,000 example sentences, right in your pocket. With no Internet connection required. I bet Steve Jobs had this in his pocket on those frequent trips to Japan. Everything is broken down into syllables, and not only in Japanese, but also into the English alphabet. You look up words just by typing in English how they sound. That means any student with a basic grasp of hiragana can access nearly the entire Japanese language with a somewhat disciplined ear. How cool is that? No other app does that effectively.
The app uses Apple iOS's built in voice recognition, so you can also enter words with speech. And even with conjugation, so it's no problem for Japanese to look up a given entry for you.
If you're studying Japanese, the app even has kanji lists broken out for you already with levels N1, N2, N3, N4 and N5. And you can create your own lists. I create lists for all sorts of things, from new words I learn on various outings in Japan, to vocabulary specific to my older son's Japanese education. I even have a list created with the kanji my wife and I lovingly and painstakingly picked for their first names, which was handy for me to refer back to as I practiced writing them to commit them to memory.
Once you get a little more advanced in your Japanese writing, the handwriting recognition feature is fun and incredibly effective. Sometimes it's easier to write a character, especially if you don't know how to pronounce it. This has been a game-changer for me when I'm reading a magazine, newspaper, or just out and about anywhere in Japan. Just tap to switch to handwriting mode and draw the character, and voila. Pure magic. This is the kind of magic that iOS is all about.
Japanese by renzo Inc. is an indispensable tool for anyone in or around the Japanese language. I can't recommend it highly enough.