I'm looking for a good iPhone app to record my playing along with BIAB. For high quality recordings (e.g., demos), I use BIAB's audio recording feature and plug my guitar straight into my PC. For practice sessions, I'd like to be able to record on my iPhone so I can listen to how I sound. I've tried a few voice recording apps but the sound quality is pretty bad, despite their assurance of high fidelity. Any suggestions?

It's not the app, it's the mic.

Thanks, Matt. I suspected that. Do you just plug a good audio mic into the iPhone, or do I need some specialty mic?

Don't expect good quality out of an app. A phone is not a recording device for good quality recordings. It works fine as an audio notepad for voice but not music.

There are some Apple products specifically designed for recording.... buy one of those.

I've heard nice things about the Apogee One... http://www.sweetwater.com/store/detail/OneiOS

While I normally record with my home studio which I use Sonar Platinum. But there are times when I will go portable when at band practice. I don't use my iPhone but use a Ipad for this. The app I use is a pro 48 track DAW called Auria. You can find it here.
Auria 48 track DAW
I agree with Mat, it is not the app but the mic and interface to the iPhone. I just recently purchased the IRig Acoustic mic and running it into the Amplitube acoustic app . I then use a app called Audiobus to route the signal between the iRig acoustic app and Auria DAW.

If you are recording Electric guitars I would recommend using a interface to the phone such as what Guitarhacker pointed out or something like this iRig HD . There are lots of mics and interfaces for your iPhone out there.

I think you will be amazed at the quality of the sound you can get out of these devices.

Brian

Another vote for the Apogee One.

Here's an iPhone Life article about the subject. http://www.iphonelife.com/content/top-4-external-microphones-iphone

If you have a USB mic already (I have the Samson meteor consensor mic) you can buy a camera adapter from the Apple Store (about $40 I would say) and use your USB mic with any recording app. The results are amazing.

See if you can tell the difference?
IRig acoustic

For a basic app, I've found Voice Record Pro to be very good. It has a "High Record Quality" setting and is easy to use. Even with a simple computer mic plugged into the iPhone/iPad, the quality is serviceable for practice review.
(For better quality recordings, I still use the BIAB "record audio" feature, with my guitar plugged straight into the computer tower. I realize that doesn't work for non-electric instruments where a good quality mic would be necessary.)

On the higher end, Shure now has a stereo high-quality mic and app. I haven't tried it yet. The connection looks solid, something I haven't liked about a few others I've considered.

http://www.shure.com/americas/products/microphones/motiv/mv88-ios-digital-stereo-condenser-microphone

I have a BLUE Mikey Digital mic for the older iPhones. Quality is pretty decent given what I paid for it and the compact convenience. Rode also make a mic that was a more proper x-y pair than the BLUE.
http://www.rode.com/microphones/ixy

As for quality of mixing inside of the iPhone, there's plenty of good mixing tools - Garageband is a great place to start. Quality can be as good or better than what you can do with your computer. The 'smart instruments' in Garageband are somewhat akin to the midi BIAB accompaniment, though with less variety.

-Scott