Org
org-mode
The "killer app" for emacs is org-mode. Org-Mode is for keeping notes, maintaining TODO lists, doing project planning, outlining, and authoring with a fast and effective plain-text system. It can also be used to log time spent on projects. On top of that, it also offers a convenient way of doing literate programming. Plus it contains a spreadsheet.
Crucially, everything in Org is plain text with only very simple, human-readable markup, such as asterisks to denote heading levels.
Org-Mode is distributed with Emacs, but you may want to check for a newer version. This project is under very active development.
Mobile versions containing a subset of Org's features are available for iOS (iPhone/Pad/Pod) and Android.
Documentation
The Org-Mode project maintains excellent documentation and has an active community.