A 4(+)-track in your pocket
Next, there's a new(ish) app called Loopy ($4.99US in the App Store). It provides an amazingly slick interface for recording, looping, merging and mixing multiple tracks of audio. I've been using it in combination with my V-Moda Vibe Duo headphones with built-in microphone. The audio quality is nothing to brag about, but still surprisingly good. I love Loopy's interface, which represents each track as a rotating platter. The timing is automatic on the loops, based on the tempo you set (the time signature is quite flexible). It can be a little tricky to start and stop recordings in time to get the automatic timing right; it's a bit of a fumble from playing the last chord to hitting a small spot on your iPhone screen. Loopy is pretty smart about short delays, though.
You can start by tapping out a tempo on the small counter at the bottom, which also functions as a button to turn the metronome on and off. Touching once on a blank track begins recording, tapping again stops, and pressing and holding reveals four buttons on each track for functions like clearing and merging. Running your finger around in a circle on a track allows you to individually set a volume level for that track. Recorded tracks keep looping while you build over the top of them (they can be muted with a tap). Once you have a few tracks and the mix is right, you can drag platters together to merge them and free up more recordable tracks. I haven't gone beyond about seven tracks yet; recording through a phone mic with acoustic instruments piles up background noise pretty quickly, and ghosting is a problem.
With my current setup, Loopy doesn't produce tracks I'd phone home about (a reflection on my input device, not the quality of the app), but it's an excellent way to get an idea out of my head and start evolving chorus, verse and bridge parts. I'm quite certain that -- with a better microphone -- this app could produce tracks which no one would believe came from an iPhone. Loopy provides a built-in web server which you can access with a desktop web browser on the same wireless network to grab full mixes and individual tracks.
Old-school sequencing, new-school tech
My other favorite tool right now is a step sequencer called BeatMaker ($19.99US in the App Store), the latest version of which adds much more power and stability. It allows you to create kits with up to 16 pads, and then sequence notes within patterns and patterns within songs. Patterns (as of the new version) can be of varying lengths, and the steps can get down to finite resolutions. It has built-in effects, mixing, and even some limited sample editing capabilities. Kits can be created on your Mac using the BeatPack software available at the website, and finished recordings can be transferred back to your machine for further production.
BeatMaker supports audio recording, and provides some tools for working with live tracks. Because Loopy can export individual tracks, you can also record phrases with it and take advantage of the intelligent looping tools. Then you can turn them into BeatPacks on your Mac, transferring them back to BeatKit for extended song production and sequencing. While recording live audio is more fun in Loopy, I can tell you from experience that it's a lot more fun to sequence rhythm sections in BeatKit than it is to try to emulate them by beating on an acoustic guitar.
This is obviously just a brief overview of some great apps with a lot of potential, and a combination which I've found to work well. I'd love to hear comments from other musicians about which apps are the most helpful to you.