The paper business card may go away someday if innovative apps like Bump and Evernote Hello take over, but for now we're still dealing with these little chunks of cardboard. Of course, in almost all cases it's not the physical object we care about, but rather the data printed on the card. (Some exceptions are inevitable.)
Getting those inky bits converted to actual bits is easy enough with your iPhone and the right app. My default tool for business card scanning has been CardMunch, which has a number of advantages: fast, ties in easily to parent company LinkedIn, accurate (using actual humans to do the card transcription) and free. Unfortunately, CardMunch's cloud dependency means that sometimes it can get backed up, and when you're sitting on an airplane with a stack of post-conference business cards to go through, it's quite likely useless.
That's where the Penpower family of contact management apps comes into play. The flagship iPhone app is the US$6.99 WorldCard Mobile, and it picks up nicely where CardMunch leaves off. You can scan your cards neatly without any network connection, and all the OCR processing is handled locally on the phone. Additional features include the ability to copy an email signature and parse it into a contact record, which is a lot more useful than I thought it would be.
How good is the OCR function? Well, you can test it yourself with the app's lite version (allowing three scans the first week, and one scan per week after that). In my evaluation, I'd give it a B+ compared to the intelligent transcription of CardMunch -- keeping in mind that CardMunch also makes mistakes on some cards. Given that it's working in disconnected mode, the slight loss in accuracy seems to be a reasonable tradeoff.
What's a little harder to take is WorldCard Mobile's UI, which has the same weird aesthetic and hinky buttons as a lot of other utilitarian apps on the App Store. It compares unfavorably to CardMunch's clean look, and it's most reminiscent of the early versions of Readdle's apps (which have come a long way since v1, in fairness). The lite version will let you know pretty quickly whether the look will make you nuts or not.
Penpower also has a WorldCard Contacts app, which lets you keep the card images alongside your contact records but omits the OCR tool; it's $2.99. There is an iPad version, too, which costs $14.99 and doesn't quite work as advertised with the iPad 2's onboard camera, per reviewers -- it's apparently not quite high-res enough for accurate recognition.
If you're a frequent business card recipient and you'd like to be mobile-enabled, check out WorldCard Mobile; start with the lite version, and if it's useful you can fork over the $7 for the full build.