(Note – these all work on the iPad, I believe)
DropBox (Free)
Seriously: If you don’t already have this, stop whatever you are doing and download it now.
Install the PC, Mac or Linux software on any computer and you can have a single directory that automatically synchronises to any computer you wish. You get 2GB of free space, and can upgrade to 100Gb for a pretty reasonable fee
Then install the free iPhone App and you can access your drop box from your iPhone. Loads of supported file formats.
iStockphoto (Free)
Instant access to a database of millions of royalty-free images. And it’s faster than the website as well.
iSSH (£6)
A VT100, VT102, VT220, ANSI, and xterm client. It does SSH. It has a VNC client. You can do X server connection. All the usual RSA and DSA key options. It is so ridiculously clever, that if you are a system administration and find yourself thinking “blimey , six quid is a lot for an iphone app”, then slap yourself on the back of the head before you buy it.
ePrint (£2)
Print from your iPhone to any Postscript LPR/LPD device (mostly) by IP Address. . Then chortle, because it’s so clever. I don’t chortle very often, but printing off a contact from my iPhone to a nearby networked printer definitely brought on a chortling impulse.
JotNot Scanner Pro (£1)
Scan stuff with your iPhone, and send it to Google Docs as a PDF. There are more expensive alternatives with better Optical Character Recognition (OCR), but this one works for me.
Shredder Chess for iPhone (£6)
Pocket-based chess humiliation by one of the world’s strongest chess engines (2600 ELO). Can be dialed down to 850 ELO (Carbon Monoxide Poisoning) if you want to even the odds. Best chess app on the iPhone, with the edge over Fritz due to the inclusion of loads of chess puzzles.