Is there a time tracing web application?
On the other hand, if your question is about measuring the response time of your web application, there are other proxy recorders besides Firebug: SST Trace Plus and Fiddler come to mind. Fiddler is open source and you can write plugins for him.
If you are serious about measuring response time, you want to do it under very high loads, though, to find the breakpoints of your system / application. There are no good free tools, and most people use HP LoadRunner (for large functional tests) or Spirent Avalanche (for very high loads).
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Do you mean a time tracking tool as a developer, or a tool for monitoring how quickly your program responds?
If you want to track your time, try base camp ( http://www.basecamphq.com/ )
If you want to track application performance, then @RichieHindle's suggestion (Firebug, answer now deleted) is a good one.
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