Apple released Music Memos, a fantastic little iPad/iPhone app last month. It's free, and everyone should know about it.
Here's how it works.
The screen at the top of this post is your entire recording interface: just a dark background with a button! Tap the button, and it starts recording when it hears you start singing and/or playing.
And then all this unassuming little program does is record your singing or instrument playing, even out the timing to put it into bars, and tune it.
Then it figures out what chords you played, or what chords would work. Tap the bass and drums icons, and it automatically adds parts that work with your playing - and they're pretty good!
You can export the result into GarageBand for further work, email the audio file, or share it to a number of other places. Of course, this is where your iConnectivity interface's Audio PassThru feature comes in handy - you can bring the audio into your Mac or PC DAW very easily. In fact, if you're a Logic Pro X or GarageBand user, you can export the actual session file to your Mac via iTunes.
Now, of course Music Memos has limitations. It doesn't know about expensive chords or compound time signatures, for example. But what it does do is just remarkable.