Add a bookmark that is only javascript, not a URL
What you want is a bookmarklet they are easy to create and should work in most major browsers.
Edit: Stack overflow seems not to allow creating bookmarklets in the context of the site, basically you can create a new bookmark and type the following in the location field
javascript:window.location='http://www.google.com/search?q='+Date()
to get a bookmarklet that searches google for the current date.
It is worthy of note that you can put that in a function wrapper as well. imranamajeed nicely illustrated that for us... but apparently I'm too new to the site to up his post. :P
so for clarity:
javascript:(function(){ location.href = location.href + "#";})();
(the carriage returns did not affect performance in chrome and IE)
One minor catch. IE can only handle a 508 character URL in this format. If you save it in IE with a url longer than this, it will truncate without warning and thus fail.
If you need a really complex script, you'll need to use a "hosted" bookmarklet, where you have a short bookmark that injects a script tag into the page, to "call" your hosted bookmarklet.
It isn't as nice/portable, but its the only workaround.