I quote the ClockingIT website: "ClockingIT is a hosted application for tracking all your tasks, issues, projects and time spent, with a focus on software development and handling large amounts of tasks." And it's absolutely amazing, too.
The creators (a husband-and-wife team in Norway) have placed a heavy emphasis on efficiency, ease of use, and functionality. Every part of the task/bug workflow is fully contained within, at most, two clicks. (A cardinal rule of interface design: No more than three clicks, please.) When you first log in, you get an amazing interactive tutorial that gets you actually using the application. (I'm begging you to sign up, if only to try the tutorial. It's really a work of art.)
Bob, what are you doing in this meeting? This isn't your project!
All work is kept separate. When you sign up, you get a subdomain of clockingit.com. So, if you were to sign up with the username "example", you'd get example.clockingit.com. You can add projects, add co-workers, assign co-workers to certain projects, and give them certain permissions within their project, so you don't have to worry about people seeing projects that they aren't a part of.
Just a few bonuses
The sign-up process literally takes ten seconds. A very efficient and functional reporting system makes it easy to generate billing information, workload summaries, and other analyses of any information that was recorded. They let you add avatars for users and add a logo to replace the ClockingIT logo, giving you everything you need to use ClockingIT as your company's time tracking system. And, the icing on the cake, if you're worried about having your data on someone else's servers, feel free to download the source and set it up on your corporate intranet.
(Oh, I didn't tell you it was open source? It's open source. :D )
My experience
I've been using ClockingIT for a few months, and I have only one complaint: When you hover over a task in the list, instead of seeing the formatted description of the task in the tooltip, you see the HTML tags. And I'm not too up-in-arms about this, since the bug only rears its head in Firefox 3 betas and Internet Explorer, and the creator told me that he's planning on fixing it. (Ahh, the beauty of open development - you'll never see Microsoft actively working with its "community" to fix bugs.)
I can give nothing less than a complete recommendation for this beauty of open source. I've shown this software to a lot of people, and every one of them has loved it - I think you will, too.