How do I remove the StackEgg game from top right hand side of the SE pages?
Click the StackEgg animation in the sidebar to open the popup.
Click the ? (help and settings) button on the top-right of the popup.
Enable the "remove the StackEgg from the site's sidebar" option in the settings.
Or, it'll be gone very shortly anyway!
If you want to re-enable StackEgg, click the link in the footer: