See http://caniuse.com/#search=worker for the most up-to-date support info.
The following was the state of support circa 2009.
Apart from from Gears there's nothing available right now, but there's plenty of talk about how to implement this so I guess watch this question as the answer will no doubt change in future.
Here's the relevant documentation for Gears: WorkerPool API
WHATWG has a Draft Recommendation for worker threads: Web Workers
And there's also Mozilla’s DOM Worker Threads
Firefox 3.5 has web workers. Some demos of web workers, if you want to see them in action:
The Gears plugin can also be installed in Firefox.
Safari 4, and the WebKit nightlies have worker threads:
Chrome has Gears baked in, so it can do threads, although it requires a confirmation prompt from the user (and it uses a different API to web workers, although it will work in any browser with the Gears plugin installed):
IE8 and IE9 can only do threads with the Gears plugin installed