Kimai is a free open source time tracker web app.
It is a PHP-powered, web application that enables us to define projects/tasks and record the time we work on each item.
Although it is web-based interface it run cross-platform, the timer keeps working even if the browser is closed unless it is stopped.
It tracks work time and prints out a reports of your activities on demand. Yearly, monthly, daily, by customer, by project, by action.

The application stores the data in a MySQL database and it has a multilingual interface.
Requirements: PHP 5.2+, MySQL 4.1+
Website: http://www.kimai.org/en/
Demo: http://www.kimai.org/en/demo.html
Download: http://www.kimai.org/en/download.html