Greasemonkey should track where userscripts are downloaded from and periodically check back for updates. Updates should be presented in a manner similar to that of addons.mozilla.org (no automatic updating).
This is an intentional duplicate of ticket #45 because the devjavu trac server now fails to render that ticket (you can find evidence of it by searching for it.
Ticket #45 was initially balked at because it was concluded that most people do not share greasemonkey scripts, and the few that do would have little need for updates. I find both of these assessments to be nonsensical. The Userscripts.org community is a very strong and popular community centered around the publishing of greasemonkey userscripts for sharing. Greasemonkey itself sometimes even advocates for using Userscripts.org and I really don't see why there is not a tighter integration. Jesse Andrews is a very friendly and competent administrator there, and I'm sure he'd be thrilled at this prospect.
As to demand for updating scripts, there are several popular published scripts that hack together update features on their own (with mixed success and questionable usability), totaling well over TEN THOUSAND installs, most notably the Userscripts Updater (over 9000 installs) plus several sample scripts that allow developers to include self-updates in their own scripts (clearly, such scripts will not have representative install counts). There are also numerous threads of people requesting this feature in the forums, including this thread that references several others.
This is also somewhat related to ticket #4 (display and install available scripts on userscripts.com for the current site).