Does javascript work on mobile phones?
In general I would assume that javascript isn't there, as older cellphone models may not support javascript, but, if you use unobtrusive javascript and graceful degradation, then it won't really matter, as your page will function in some known way on any device, as long as it is formatting itself properly.
So, if you want to have it work on all mobile phones, then start with not needing javascript, then add in the javascript as an enhancement.
depends on the browser
Depends on what mobile phones and to what extent you need support.
Smart phones pretty much all include support for JavaScript. How well they support them is another story.
You can see a lot of what mobile devices support here: http://www.quirksmode.org/m/table.html
Bare in mind as well that their are different versions of JavaScript supported by different phones and different browsers, even if JavaScript is available.
Some. Do you have a specific model in mind or just in general?
I think javascript is totally browser dependent. Symbian mobile surely can run javascript. Smart phones are much smarter to handle javascript.