A specialised text editor -- or maybe a mode for an existing one -- that is designed for keeping brief textual notes. I'd want to be able to categorise notes (using free-form tags), and do fast full-text searches across all the notes (ideally based on an index that is updated as you type; it would also be possible to do remem-style relevant note matching). I'd also want to be able to run multiple copies of it on different machines and have them stay in sync. A command-line interface would be useful; the GUI should provide "instant-save" semantics.
This'd almost make a good web application, but text areas in web browsers are a bit too primitive at the moment. It might be nice to interface it to a Wiki or blog.