A double-entry bookkeeping computer language that lets you define financial transaction records in a text file, read them in memory, generate a variety of reports from them, and provides a web interface. In theory, if it can read a text file, it can manipulate your accounting "database." More of a standard or file format than an application because you can do it all in a text editor if you really want.
The reference implementation is written in Python and seems to have a webapp.
Fava is a web interface for the double-entry bookkeeping software Beancount with a focus on features and usability. Generates expense reports, graphs, tracks your money, assets and accounts, even lets you run queries. Has an API but it's for internal use only
Appears to be a personal scrobbler server written in Python. Seems to require Postgres as its database. Implements the Audioscrobbler API.
A simple, fully responsive Dashboard to forward to the services of your choice! Ideal for Desktop and mobile usage! Add all of your services, whether you host them yourself or not and display them as neat Icons from the FontAwesome libary. simple-dash is made to be as simple and minimalistic as possible.
A personal file system indexing and search application. Part of the Gnome desktop. Indexes file contents, metadata, and location to better help you find things. Also allows you to do your own tagging of stuff it keeps track of. Uses D-BUS for IPC and SPARQL for search. Uses multiple ontologies for different kinds of files (including multimedia content).
An archive of strange pranks and goings-on. Safe for work!
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Personal finance software written in Java. Thus, it'll run pretty much anywhere. It comes as a single .jar file, so you can drop it into an encrypted volume along with the data files, which I suggest that everyone do. These ARE your finances, after all.
An online personal database/social networking site comparable to LibraryThing for cataloging your comic book collection.
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An offline method of generating passwords using a randomized matrix of characters. You pick out your password by remembering a symbol, a color, and a direction. Much easier to use than it sounds.
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Want to buy Bitcoins but want to do it locally? Look to seee who's selling them near where you live (or search by zip code).
CozyCloud is an open source cloud application set that is personal, i.e., it's meant for one person to use for productivity and information organization. You set it up and it's yours, no one can take it (or your data) away from you. Comes out of the box with a webmail client which unifies all of your e-mail accounts, a notes and document editor and manager, a to-do tracker, a bookmark manager, a financial account manager, and an RSS feed reader. Includes a framework for developing new apps, which are appearing all the time. Built on top of node.js.
Cozy is just what it says on the tin - it's a personal cloud that you access with your web browser. It has a contacts app, a feed reader, bookmarks, photo album, chat client, calendar, notepad, music player, and more. An appstore is planned for the near future. Easy to set up, you can even do it with cut-and-paste. Lightweight enough that you can run it on a RaspberryPi or Linux on a USB key if you want.
A thought experiment to consider when I have more time. personal
Canonical reference documentation for the h-card HTML format.
A web application for archiving, indexing, and managing your online media content, such as your photo albums, videos, and artwork. Aims to replace Flickr, DeviantArt, Smugmug, Picasa, YouTube, and the like because you will have control over your content and thus be resistant to censorship (plus if they go down your stuff will still be available).