iPad 2 only: OfficeDrop, makers of the previously mentioned ScanDrop for Mac, unveiled a new free iPad app this morning that allows you to use your iPad 2's camera to scan documents, run character recognition on them, and upload them to OfficeDrop.
Once installed, OfficeDrop for iPad will let you browse and organise your scanned documents in to collections, see them all at one time, or search the text inside each document from the search bar. All of this takes place offline, so the app doesn't have to connect to the cloud to scan, store or retrieve your receipts, napkin notes, or printed travel directions. If you want, OfficeDrop can link multiple scanned documents into a single PDF.
OfficeDrop's new iPad app isn't perfect: it will only do character recognition on printed text and not handwriting, and it will only upload documents to OfficeDrop, not cloud services like Dropbox or Evernote (which its desktop apps already support.) Regardless, if you're looking for an iPad app to scan and save paper documents digitally, OfficeDrop is a good, free alternative.
OfficeDrop [iTunes App Store]