Mozilla's BananaBread: Cross-compiled Cube2 FPS in the Browser
It uses WebGL, the Fullscreen API and the PointerLock API to provide a real first-person-shooter experience in the browser without plugins. It currently has doesn’t have fallbacks for missing features, so you’re best bet to use Firefox, although the demo should eventually run in all WebGL supporting-browser.
It’s not a finished demo, but rather is designed as a test-case for Firefox browser performance and will continue to be developed.
You can read more on the Mozilla Hacks Blog at Mozilla and Games: Pushing the Limits of What’s Possible or check out the code on Github.