I named this "The NEW Favorite Apps (...and that neat app you just found) thread" because there was already a "Favorite Apps (...and that neat app you just found)" thread, although that one was specifically for the iPhone and the last post was in 2011 and this one is for the iPad (though iPhone apps are welcome), but because mainly I didn't want to risk the fury of the Necro-Post Police by posting in the original four-year-old thread.
DocScanner + OCR Free is my new, favorite toy and can be found
here. With this app my iPad has pretty much replaced my desktop scanner. Full disclosure here; the vast majority of my scanning jobs involves quotes from books and not entire documents, and I have yet tried to scan an entire page and don't know how well it would do, but for the bulk of what I do it is far more convenient than firing up the desktop pc and scanner combo. Much faster, too, and at a much better price. The thing is free, but limited and full of ads, so I upgraded to the full-featured Pro version for $5. Try getting a scanner and OCR software for your pc or Mac for that price! And no, I don't own stock in the company, I just LOVE their app!
What's YOUR favorite app?