<p>I've got quite a few GreaseMonkey scripts that I wrote at my work which automatically log me into the internal sites we have here.  I've managed to write a script for nearly each one of these sites except for our time sheet application, which uses HTTP authentication.  </p>

<p>Is there a way I can use GreaseMonkey to log me into this site automatically?</p>

<p>Edit: I am aware of the store password functionality in browsers, but my scripts go a step further by checking if I'm logged into the site when it loads (by traversing HTML) and then submitting a post to the login page.  This removes the step of having to load up the site, entering the login page, entering my credentials, then hitting submit</p>

Why don't you use Firefox (I assume you're using Firefox) to remember your credentials using the Password Manager?
I found this link:
HTTP Authentication with HTML Forms
.  Looks like you can use javascript to do HTTP authentication.  I don't think you can have Greasemonkey interrupt when you are first navigating to a URL though.  You might have to setup some sort of launching point that you can use to have greasemonkey automatically redirect + login.  For example, you can have the local page that takes the destination URL in the query string, have Greasemonkey automatically do the authenticate + redirect.  The only problem is that you'll have to wrap the site bookmarks with your launching page for the bookmarks you use as entry points.