I just tried out the business card scanner from LinkedIn called CardMunch. Loaded the App on my iPhone and scanned a few cards. I have tried other such scanners and they often require editing the contact data afterwards. CardMunch was perfect the first time, apparently because there are people analyzing it on the other end. Complaints in the reviews say it can take too long to do this, but mine came back in a minute or two via notification. Automatically links to LinkedIn if you want to. Loads the contact on your phone. Simple interface, good experience so far.
Update: You cannot get a card into this system easily unless you have access to a physical card. Also you are relying on Linkedin to keep this data safe, so I am not quite ready to throw out the physical cards. Also the syncing between the entries on multiple devices seems haphazard. Still waiting for some to happen ...
Update 2: Hours later now I still have 5 business cards 'in process'. Slow indeed. But you could say that this is sufficiently fast for recording a card, I probably do not need the data immediately. I can get nearly instant image character recognition with other Apps, but I usually have to edit that. Several commenters suggest that they use Amazon's Mechanical Turk to read the scanned cards. Which could be a cause for the delay.
Update 3: It seems the problem I was having were due to publicity and thus server or analyst overload. My cards are returning in less than 15 minutes now. If that continues, CardMunch is an excellent product.