I wanted to go to a specific time on a YouTube video, and headed over to youtubetime.com. It wasn’t there. Or at least, it seemed to be ads instead of the page. I manually entered the code to the URL (#t=0m40s) instead.
If you’re on a video on YouTube itself, and you click the “Share” button, it gives you the option of setting a “start at” time and the resulting link will include the timecode.