There are many open source apps out there, its just not so easy to find them all and pick the gems. I hope it helps a bit

iOcticat by Dennis Blöte (MIT)

Parses data from github.com. Uses ASIHTTPRequest and TouchJSON (from touchcode) for the http layer. Uses Gravatar code. Nice Gui, No persistence.

Not really documentated, but the app is under active development, and you can drop dennis a line.

TwitterFon by naanstudi (GPL)

“Simple, Clean, and Fast Twitter Client for iPhone and iPod Touch.”TwitterFon _was_ open source up to version 1.4.1. Current is 1.5.1, nevertheless you can learn a lot: Twitter API, custom search views, progress window, a web view controller (like MobileSafari), an ImageStore, JSON, Regular Expressions, Core Location – and Chat Bubble View!

Database Connection is done via raw sqlite, even with a model migration script.

Mobile Colloquy by Jane Lee (Licence?)

IRC Client for the iPhone, based on Colloquy for Mac OS X.

Very interesting! Has features like nickname and emoticon completion popups, Highlights messages (and optionally vibrates) when your specific words or nickname is mentioned, landscape mode, stay connected while iPhone is locked, SSL.
Unicode framework(libicucore), Base64-Encoding, InterThreadMessaging, Sockets.

Other Apps worth mentioning:

• WordPress for iPhone (GPL): XMPRPC, CoreAnimation, KeyChain)
• wikiHow (MIT) : Image Resizing, Flurry Analytics, sqlite, Google Toolbox
• NatsuLiphone – Twitter Client (Accelerometer, …)
• Molecules (BSD): View three-dimensional renderings of molecules: OpenGL, GZIP
• Barcodes (Apache 2.o): Scan Barcodes.
• RemotePad (New BSD): Remote Control your Mouse, with MultiOS-Server.
• AppSales-mobile (New BSD): Analyze sales from iTunes Connect
• Apps Amuck: 31 small iPhone Apps
• Wolfenstein 3D: do i have to say more! OpenGL!
• Tris: (Artistic/GPL) Tetris for iPhone (quite old)
• metasyntactic has quite a lot: NowPlaying, YourRights, ProtocolBuffers and PocketFlix -  frontend for Netflix.

Components, ready to use:

• Three20 (MIT; components from the facebook app)
• editorrific (dynamic text editor component)
• flicktabcontrol 1 and another one (like the one in the facebook app)

And don’t forget all the hot frameworks!

• GoogleToolbox for Mac (Apache Licence 2.0; Unit Testing, many code snippets like html escaping, logger, …)
• TouchCode (MIT; JSON, XML-Parsing, HTTPD-Server, …)
• ASIHTTPRequest (BSD; easy wrapper around CFNetwork for REST-based services)
• Flurry Analytics (Real time user data)
• cocos2d-iphone (LGPL; framework for building 2D games)
• gh-unit: test framework, can be used with SenTestingKit, GTM or by itself.
• high-level cryptography API
• TDParseKit – Cocoa Objective-C Framework for parsing and tokenzing
• simple-iphone-image-processing
• fixed length queue of elements for UITableViewController
• FunctionalKit: It’s Functional for Objective-C.
  

Other Useful bits:

• Sample project using the ASIHTTPRequest to load the public Flickr RSS feed, and then load the images in a UITableView in asynchronous fashion
• font browser
  
• Some nice features of the objectivec language
• 10 iPhone memory management tipps
• Open Source iPhone Directory
• http://www.codingventures.com/2009/04/more-useful-open-source-libraries-for-iphone-development/
• http://iphoneresources.aribraginsky.com (TOP!)
  

Something’s missing? Please drop me a line!

Btw: I really like the idea of open sourcing the app _and_ charging money for it. You help other developers building better apps while getting some refund for your work. Thats possible thanks to the iPhone Developer Program – unsigned apps won’t load on the phone, and apple changes 99$/79€ for it.

Related posts:

1. Open Source iPhone Gems, Part 2
2. Tweetie like swipe menu for iPhone apps
3. iPhone gaming framework