Casio has launched two nice iOS apps. One of them "Chordana Viewer" is a very cool app which detects the chords from an audio file.
I tested it and it got the chords right for 4 out of 5 songs. It may not be the perfect audio chord recognition out there but it definitely gives a head start for those who want to learn a new song.

More on this => Casio iOS Apps

Band in the Box 2012 and Powertracks 12, will both do the same..

Anybody know what's the MOST accurate app (either regular OS or iPad/Surface) for this ability?

I am on the lookout for such a software too. From whatever apps I have tried, all are at around 70-80% accuracy. The songs with prominent bass lines and major chords gets detected accurately but the accuracy drops when it has inversions or dominating lead instruments.

The spectral analysis of the audio signals need really good algorithms than merely identifying based on the frequency range and harmonic content. Unlike audio, MIDI world is so much better; it obeys whatever its told to do.

The BIG three have the money and the R&D to get it right. Let`s hope we get such a feature in our arrangers. And this would be great if its a software only upgrade. Oh well ...

Chordify has helped me a lot.

Thanks Fran and Trident. Never knew that the software from PG Music had these features. And am new to chordify as well.

I checked it only for a couple of songs on you tube links and its pretty fast and reasonably accurate at detecting the chords.