Lets build great collection of the most useful app on your iPhone/iPad, let me start first what I have installed:

FREE
-Tae Kim grammar app

PAID
-Japanese (dictionary)
-Flashcards Delux

Paid-Midori <-- Japanese dictionary

A bunch of them here:
http://rtkwiki.koohii.com/wiki/IPhone_Applications

I've personally found the Monokakido Wisdom J-E and Daijirin J-J dictionaries to be well worth the money and have been using them for years.