I am a happy owner (and developer) of an iPhone and and iPad and love to learn about new/cool/exciting apps. This thread is quite simple; just post a picture of the homescreen of your favorite iDevice and explain why each 3rd party app or folder (or only ones you deem important) deserves one of your 20 spots on your homepage. In case anyone doesn't know, you can take a screenshot on your iphone by pressing both the home and lock buttons at the same time.
I'll start:
Utilities Folder: contains important utilities such as Bloomberg (stocks), DropBox, Pastebot, Find my iPhone, and Sleep Cycle (my alarm clock).
Calcbot: My preferred iteration of the calculator for the iPhone. It saves your calculation history and has a gorgeous UI.
Apple Folder: contains most of the built in apps (iTunes, Clock, Notes, Compass) that I don't use as often as the ones that are not in that folder.
Things: A great task manager that I use to organize my HW, and other random tasks. It syncs with a version for my Mac and iPad.
Reeder: My favorite RSS reader. Syncs with Google reader, and also has an iPad version which has a stunning UI.
Rdio: A subscription music service I am trying out.
Dock: Default [Phone - Mail - Safari - iPod] setup that iPhones ship with.