Here is a list of some of the iPhone/iOS open source projects that I have found useful and/or cool:
FMDatabase by Gus Mueller
I have been using this project for a very long time, and found it to be an excellent way to use SQLite without really using SQLite. If you need access to data on the device, and you do not want to mess with Core Data, this is without a doubt the way to go.
MBProgressHUD by Matej Bukovinski
This library allows you to easily present the iPhone equivalent of the wait cursor on the screen for lengthy operations.
iCarousel by Nick Lockwood
I used this library in the iFleet application to provide a much nicer photo browsing experience. Unfortunately, when you are pushing a bunch of large images to the iCarousel class, it does tend to slow down, so I created the view by default with the correct number of subviews for my photos, but the view start out all blank with an activity indicator. Then, I use GCD to load the photos into views in the background, and when a view is ready, the background thread informs the main thread to update the control and the photo views slide into the control.
All in all, this is a very cool class.
TPKeyboardAvoiding by Michael Tyson
I always hate setting up and monitoring for the keyboard appearing and disappearing, and manipulating the view frames and visible table view cells, it seems to me like something that should automagically happen on the device. Well this class appears to do a very nice job of automating this very task.
iDevRecipes blog source code
They have some nice examples on how to do some very nice UI things, such as using images in a navigation bar and custom back buttons.
Textor by Louis D’hauwe
This is the source code to an iOS text editor application that was available in the App Store.
Other useful controls
NYSegmentedControl by Nealon Young — a nice drop in replacement for UISegmentedControl
SideMenu by Yalantis — animated side menu with a customizable UI