SharpScan is a free (with in-app purchase options) iOS app that makes document scanning a snap. Select your camera to snap a document or choose an image with text already saved in your camera roll, and you'll quickly get a sharp image of your document. The app helps knock out noise, shadows and those inevitable distortions that arise from shooting at a slightly off-center angle.
The image can be cropped manually or automatically. Scanned documents are then shareable as an image file or a PDF. The free version is ad-supported, and it also adds an unobtrusive watermark to your scanned images. You can upgrade to the pro version for US$2.99.
I ran SharpScan through a variety of tasks, and it worked quite well. I even scanned an address and turned it into a label that I printed and attached to an envelope. Text was sharp, and the app focused quickly on the documents I was scanning. Help is built-in, and there are video tutorials available, but I think most users will never need them.
In my opinion, the only negative thing about SharpScan is that there is no optical character recognition (OCR) capability. You're always going to wind up with an image, not editable text. For many users, that will be enough. For those who want more, I suggest a look at Image to Text (free), a clever app that scans documents and performs recognition to convert those images to editable text. I've also been impressed with Prizmo, a $4.99 app that scans, does OCR and can even read a document to you aloud.
If you want quick scans, SharpScan is very useful. I didn't mind the small ad or watermark in the free version. If your scanning needs are more ambitious, you will find many alternatives at the App Store. The app requires iOS 6 and is optimized for the iPhone 5. It also ran fine under iOS 7 beta 6.