One of the shinier apps out there for the iPhone is EVE Tracker from Saggy Software, an application that also runs on the iPod touch. As its name implies, EVE Tracker can track a pilot's stats and training status; it displays your avatar and isk balance, in addition to your attributes and skillpoints. You can review your character's skill progression (skills previously trained) and flip through related info with a skill browser. EVE Tracker can handle multiple characters and multiple accounts, which could be handy for those who took advantage of EVE's Power of Two subscription offer a little while back.
One caveat about EVE Tracker (as shown on its iTunes App Store page) is that your account must be active in order to use its pilot tracking features -- so those who stop paying for their capital alt account while training up Gallente Carrier 5... this app is probably not going to help you.
EVE Tracker needs your limited API key, which is a simple matter to find (and if you're using EVEMon -- and we hope you are -- you already know how to use this.) The downside, which people have mentioned on the EVE forums, is that the iPhone's lack of copy-paste means that that long API string will need to be entered manually.
A few EVE players have commented that they're having problems getting EVE Tracker to run on their iPhones, but others seem to be faring well. The app is free so it might be worth a look if you've got either an iPhone or iPod touch. Check out the developer's site for more details and a gallery of screenshots showing the app in action. Of course there are other competing apps out there. Are there any others that you swear by?