Installing this plugin: Clone the repo (or download the .zip file, or whatever). Go to Extensions->Load unpacked extensions and choose the folder.
You'll be all set! Now there will be a neat checkbox under every YouTube video. When it's checked, that video will never appear in your "Related" feed ever again.
Be sure to edit newtube.js if you don't want the data synced with your Google account.
The plugin is also on the Google Web Store.