User Script Hosting
Gist
Gist is GitHub's "paste" service, where any set of simple files can be pasted into a web form and saved.
Gist files may be named. If they are given the .user.js suffix, then the raw link for the gist will serve perfectly as an install.
HTTPS is available and used by default.
Greasy Fork
Created by the maintainer of http://userstyles.org/. HTTPS is available and enforced by default. Open source, hosted on GitHub.
OpenUserJS.org
"An open source user scripts repo built using Node.js". Only HTTPS is available. Open source, hosted on GitHub.
MonkeyGuts
"MonkeyGuts is a brand-new script repository." Only HTTPS is available. Closed source for now.
UserScripts.org
One of the original and longest running user script hosting sites. HTTPS is available but not used/linked to by default. As of 2014, largely fallen into disrepair.
The Whole Internet
Any server across the entire web may host user scripts.
For Greasemonkey, the only requirement is that the (entire) URL ends with .user.js and that it is not served with a text/html content type.
Servers supporting HTTPS are best, in order to be compatible with Greasemonkey's built in update checker.
