If you enjoy anime or Japanese drama, then Crunchyroll is far and away the best app on the App Store to feed your obsession. The app is very simple in execution but delivers above and beyond what you would expect for an app that is free to use and contains so many different shows dating back more than a decade. With simple, intuitive menus, a universal app for access on your iPad or iPhone, and a free version that includes hundreds of episodes, it's a great place to start if you enjoy anime or are interested in getting into it.
Upon installation, you can choose to create a free account, which requires only an email address and password, or you can continue using the app as a guest. Free registration allows you to track your watching history and create a queue of episodes you would like to watch in the future. There are hundreds of shows to choose from, at first, though keep in mind that newer episodes of any show will require a Premium Membership. With the $4.99/month premium membership you can watch shows up to an hour after they premiere in Japan, watch over your cellular network, and see no ads, so it's the way to go if you plan on using the app a lot. But even for casual users, the app is powerful with a free account.
You can sort anime alphabetically or by popularity, date, genre, or season and you can then sort through each season of a show quickly and easily. There is a search function, as well, and all of the drama and anime have been separated into different menus for ease of access. Ultimately, Crunchyroll is the best way to watch anime on your iPad or iPhone, both in terms of cost and total access. Keep in mind that all shows are subtitled, with the original Japanese voice tracks; but if you are okay with reading subtitles, you can't get a better fix for your anime obsession.