Well forever is a _really_ long time, but I wouldn't be too surprised. I mean we still have significant banking infrastructure running on Cobol.
Hopefully browsers will ship with native support for something better, in addition to javascript. A common virtual machine that you could run your code on would be awesome. You can kinda do that today, except JS makes a terrible VM spec.
Probably, as javascript will remain the browser's only supported scripting language forever as it's such a big hurdle to get all the browser makers to implement a new language. I imagine javascript in the browser will eventually be like x86 assembler though in that almost everybody will write in a higher level language like coffeescript, or through layers of libraries like jQuery.