After years of constant user requests, Google has finally decided to heed the community's voice and add a native option in YouTube's interface that allows users to loop videos without using extra software, browser extensions, or third-party websites.
The option called "Loop" was added to the hidden menu that appears when you right-click on a video's surface. You can currently find Loop as the fourth option down the menu.
Selecting it will automatically loop the current video, indefinitely, until you navigate away to another page, or you close the browser tab.
The looping option is not permanent and is not stored in a cookie or YouTube settings area. This means that returning to a previously looped video, the option will be unchecked, and you'll have to enable it again.
Previously, the easiest way to loop a YouTube video was by adding "repeat" in a YouTube URL, like: "youtuberepeat.com/watch?v=XXXXXXX"
This trick would redirect users to the ListenOnRepeat website, which automatically would reload a page whenever a YouTube video would finish playing.
The Loop option is not yet available for YouTube's mobile apps. Google hasn't officially announced this feature through a blog post or tweet, which possibly means it's still in its testing phase.
If you can't find the Loop menu option, here's a screenshot to help you out.