There is an app for iOS that is simply called Japanese. It's by Renzo, Inc and is probably my single most valued resource at the moment (aside from Jpod, もちろん。)
It is basically a dictionary but has many great features. You can search words by English, romaji, kanji or kana. It will usually find the word you want even if you enter it in a conjugated form. Dictionary entries include all conjugations, romaji, kanji, kanji alternatives, kanji breakdowns (with animated stroke order) tons of example sentences (with furigana!)
There is a search history, which is great when you look up a word then later can't remember it (like me.) You can add notes and make word lists. Tap the kanji that float by on the Discover screen and be taken to it's page. There are options for studying vocabulary and kanji. Browse words by lexical categories or classifications. There is a JLPT section, but I haven't used that yet...
Switch to Japanese input and speak the word you want to look up. Hell, speak the whole sentence, the dictionary will do it's best to break the entire thing down and display the words.
It's about $5.99 on iTunes, I use it literally EVERY day. About the only thing I could see making it better would be if it could speak. I would love that, and maybe record your voice and let the app judge your pronunciation... That would be awesome.
I have no affiliation with the makers of the app, I usually don't even review or rate apps. This app is just THAT good, I have to spread the word a bit!
Their site: http://japaneseapp.com/
iTunes link: https://itunes.apple.com/us/app/japanese/id290664053