All modern web browsers (I'll try not to troll about IE) support web workers. However, the semantics of web workers is message-passing (by copy, most of the time), which is the semantics generally associated to multi-process rather than multi-threading. Most developers using threads expect some kind of memory sharing, which is impossible with web workers at the moment.
Shared workers (not implemented in any browser atm, I believe) will take care of some usage scenarios. Other alternatives are being explored (e.g. [Parallel JS](http://smallcultfollowing.com/babysteps/blog/2012/01/09/para...). However, for the time being, don't expect any support from JS to do shared memory concurrency.
Note: I'm a Firefox dev.
Of course this was in the early days, and it'd be good to retest it to see if it's better now.
I think that there are a lot of interesting use cases for WebWorkers, but you also have to be aware that for some things they will actually slow down your application.
Related: Why does it seem like web workers don't exist? I can hardly think of any popular libraries or web apps that make use of them, despite the seemingly obvious utility.