1. 'Band' (£5.99) by MooCowMusic - a 'band in a box' type app, with 12-bar blues riffs, a drum kit, funky drummer riffs, and keyboard... you can record and use basic edit functions, or jam along to an existing recording, and overlay on top of it. This is so much fun it's indecent. The attention to detail is superb, and at £5.99 it's a steal. MooCowMusic also make 'Pianist' which is similar only just a piano, a much more fully-featured one than in Band, with full 88-key keyboard, sustain, soft, pan, and so on... again the attention to detail is superb, and it's only £3.49.
2. 'Shazam' (free) by Shazam Entertainment Ltd - this is the iPhone version of that thing where you dial a number and hold the phone up to a radio (etc) and it tells you what the track is. I can't believe how good this is... I was in a pub the other night, two rooms away from the disco, with a bunch of noisy pissheads in both rooms, and it was still identifying track after track. It's very accurate as well... it never gets the wrong artist when it's a cover version. After identifying the track it allows you to purchase it from the iTunes library, which is presumably how they fund the app, and you can tag it with a photo you take on the spot... nice touch!
3. 'Midomi' (free) by Melodis Corporation - very similar to Shazam but also identifies songs from humming, whistling and singing, as well as searching for artists or tracks from voice input. Whistle the first two bars of "somewhere over the rainbow" to it and it lists a whole bunch of versions, with Judy Garland at the top. Which is nice. It's nowhere near as accurate as Shazam when sampling an actual playing track, also the interface is not as good as Shazam.
4. 'Maps' (free) by Apple. Built in app using Google's mapping API. The GPS functionality and integration with the maps API is superb... lovely looking and very fast to locate because of its Assisted (by cell phone mast and wi-fi triangulation) nature. It's not a full-blown sat nav, and could do with Tom-Tom like satnav features, or maybe I just haven't found them.
5. 'Last.fm' (free) - by Last.fm, the iphone incarnation of Last.fm, the excellent instant personalised radio station service. It's so good you almost don't need to put your own tracks on your iPhone.
6. 'Starmap' (£6.99) by Fredd. I haven't used this sky mapping thingamajig extensively but I have high hopes for it when I reach the dark skies of Italy in a week or so. I hope it may double my astronomical knowledge in about five minutes.
7. 'SignalSuite' (£5.99) and 'SignalScope' (£14.99) by Faber Acoustical. These are quite expensive especially the Scope application, but when you consider their quality and what they are actually doing, it's really not that much to pay. SignalSuite is an audio signal generator, with three types of output waveform, all usable together, programmable sweeps, white and pink noise generators, and loads more. SignalScope is a full audio spectrum frequency analyser that can use the built in mic, a headset mic, and even the iPhone's accelerometer as inputs. It has a zillion configuration options and is very easy to use. My only gripe about these two is that you can't output pink noise using SignalSuite at the same time as using SignalScope to analyse it coming out of your speakers. I'm sure if this was possible they would have made it so... but I'm going to mail them about it anyway :-)