I prefer to keep as little paper as possible, so I do a lot of scanning. I haven't yet splurged on a ScanSnap, so I do most of it from my iPhone or iPad. My choice for the last year or so has been Scanner Pro by Readdle. I also use their great app PDF Expert for most of my grading, paper reading, and editing. If you absolutely refuse to spend a few dollars on an App, the new Evernote Scannable looks nice.
Below is a list of the apps that I've tried over the past few years, in rough order of preference/recommendation. For a more thorough review, I suggest that you check out The Sweet Setup.
|App||Free version?||Android version?|