Tampermonkey is a free browser extension and the most popular userscript manager for Blink- and WebKit-based Browsers like Chrome, Opera Next and Safari.
Even though some of the supported browsers have native userscript support, Tampermonkey will give you much more convenience in managing your userscripts. It provides features like easy script installation, automatic update checks, a simple overview what scripts are running at a tab, a built-in editor and there is a good chance that incompatible scripts run fine with Tampermonkey. More Info »
Tampermonkey is available for Google Chrome, Opera, Chromium, a lot of their derivatives and also Firefox and some Android browsers.