Those interested in Japanese novels and short stories have a variety of free options available: sites like Aozora Bunko (青空文庫) which contain older titles and “Shousetsu wo yomou” (小説を読もう) which cater to newer ones.
While it’s relatively simply to just pull up stories from such sites on your desktop machine, I think many readers out there still prefer a little more book-centric experience as opposed to reading a text file in a web browser.
The app “Sukima Dokusho” (すきま読書) is designed for that very purpose–providing something a little closer to a proper E-book reader experience on your mobile iOS (both iPad and iPhone versions exist). By the way, “sukima” (隙間) means ‘gap’, and here refers to the phrase “隙間時間” (sukima jikan) which means little gaps of time in between your busy daily schedule where you can read a few pages of a book. (“Dokusho”（読書）means “reading”)
The app has a very simple interface. When you first open it, you see an empty bookshelf screen with the option to add a new story from sites like the above-mentioned ones. For example, for Aozora Bunko there are links to the most popular works, or a page where you can search by author or work title. There is also a feature to import an Epub via Wifi, though I have never used it before.
When you find a work you like, you can either read it immediately, or add it to your bookshelf for later viewing. The app does have adds, but for the most part they are unobtrusive and you only see them once in a while. The viewing UI is simple but effective, and allows you to change basic settings like colors, font size, and horizontal/vertical reading direction.
Unlike some book readers for paid books, the word lookup in this app is pretty simple (and sometimes highlighting a word can be a little tricky, though I’ve seen similar apps that don’t allow highlighting at all), but it’s generally sufficient for occasional lookup, as long as you can stand having to go through a separate menu and choose “Search the web” most of the time.
All in all, I think this is a good app to at least try once (especially for advanced students of Japanese). It currently available on the US app store for no charge.
(Note: a word of warning for Kakuyomu fans: that site is not currently available on this app, and Kakuyomu in fact has their own app for book reading which has similar functionality, with less options for font size but an arguably prettier font)