If your iPhone or iPod Touch is jailbroken, you can use the Installer.app to load and install many different applications. Below is the list of the applications that I found to be useful, fun or interesting: 

• Organizing multiple pages of applications:Categories
• Downloading/Watching YouTube movies: MxTube
• Photos alternative: PhotoBoard
• e-Book reader: Books 
• Information Lookup: weDict , iMoon , iTrac
• Networking: Stumbler, VNsea (VNC for the iPod Touch / iPhone), TouchPad Pro (VNC without the display, still very useful for music player / presentation control)
• Games: Marble , Chess, LightsOff
• Utilities: SysInfo, AcceleroLog, TouchLayer

If your iPhone is not jailbroken, you will not be able to add any of the above games until they are added to the apple store. You can always play web-based games found on AppSafari: http://www.appsafari.com