Can I pass a JavaScript variable to another browser window?

Putting code to the matter, you can do this from the parent window:

var thisIsAnObject = {foo:'bar'};
var w = window.open("http://example.com");
w.myVariable = thisIsAnObject;

or this from the new window:

var myVariable = window.opener.thisIsAnObject;

I prefer the latter, because you will probably need to wait for the new page to load anyway, so that you can access its elements, or whatever you want.