TagTime
TagTime is a time-tracking app originally developed by the same folks behind Beeminder. It is not currently under active development, but still works as far as we know. Definitely let us know if it seems to have broken!
TagTime works by asking you what you're doing randomly throughout the day. A small but passionate contingent of Beeminder users use TagTime to track hours spent on projects (and/or their entire lives), so you might hear about it if you lurk on the forum or read the beemails!
If you're interested in using it as a Beeminder autodata source, check out the link above for more information and setup instructions (warning: it is not a one-click install). If you encounter problems, you might be able to find help on the Beeminder forum.
There's also a TagTime Android app that's less powerful but much friendlier, and very easy to get started with.
If you're interested in beeminding how you spend your time, but not so interested in the randomness of TagTime or the frustration of getting it working, you could try the Toggl integration, or perhaps the RescueTime integration if you spend most of your time online! If you already use a time-tracking service (e.g., Harvest), an IFTTT or Zapier hookup to a Beeminder goal might do the trick.
Keywords: TagTime, time tracking, RescueTime, Toggl