I have a handful of books on user interface & app design, and one shining star is 'Tapworthy, Designing Great iPhone Apps' by Josh Clark. Josh takes the reader through a journey to understand what makes great iPhone apps. Josh examines how real people use their iPhone and their apps, what thrills them, how people like to get in and out of an app quickly and use it for one thing without having to think too much about it. For example he compares gestures that are known by everyone with gestures that most people never use (ie don't design for a UI gesture that only geeky iPhone experts know about). He introduces all the standard controls and talks about how to use SDK components to structure and organize the your UI in a way that will be natural for iphone users, and then goes on to show how you can dress UI components for a custom look. Josh doesn't shy away from discussing when you shouldn't use a standard interaction too, and Apple should take note: no-one likes the shake! Throughout Tapworthy there are case studies based on interviews with app designers explaining the design choices of some hugely successful apps including Facebook, Gowalla, USA Today, Things, Twitterific, & PCalc. Whether you are building for iPhone or another mobile platform, you should study this book and keep it on your shelf, its that good. Suzanne Ginsburg's 'Designing the iPhone User Experience' is another worthy read. Its 277 pages cover iPhone apps from the point of view of a UI specialist and includes tons of good advice about market research by, prototyping, testing, how to approach the overall app design, UI design, and branding. On my first look through I feared it was another manual of 'how the pros do it' that would not suit the resources of my own two person company, but on closer inspection that's not the case at all. When the author does explain bigger budget approaches she also explains low budget 'guerilla' methods. There are tips and anecdotes throughout the book drawn from Susanne's experience working on iPhone app design and UI testing. (Suzanne is an acomplished user experience consultant in Silicon Valley.)
One piece of advice about listening to designers... They have a lot to say about things you should do, and stuff you should put into you app. All those 'shoulds' are scary to an indie software developer short on time and money and focused mainly on writing code. Think of all the 'shoulds' as a menu of stuff you can consider, and then spend your time and money where it makes sense for you. Remember though, end users don't care one bit how costly or time consuming an app is, they only care how delightful, fun, and useful the app is, and your app is going to be competing against apps that have had a lot of careful design put into them.
For those of you who can't get enough I'd like to recommend a couple more design books, though they are not iPhone books. 'The Design of Everyday Things'by D Norman is an industrial design classic. As the iPone is a device you hold and touch, the app design direction of physical / real world metaphor has proved very successful for a number of apps, and Norman's book is probably the best design guidance you will find for that kind of app.
'Don't Make Me Think' is a concise and accessible book on web usability design, it has some great lessons that iPhone designers can use too that might be a little easier to learn when seen in the context of the more familiar web.
Finally a quick mention of 'Design Basics Index' by Jim Krause, which is a useful intro and reference for graphic design concepts that's helpful to those of us without training in graphic design.