These may or may not work.
Situation 1: You’re on a site that’s popular. Suddenly, it can’t connect to the server! Oh no, it crashed! What can you do?
Let Google Cache come to your rescue. Go to Google, and put in cache:siteurl. Most likely, it’ll be there.
Situation 2: The domain for a site you like has been snapped up by some dumb search engine. If you’re lucky. the Internet Archive will have it.
Simply type the URL into the WayBack machine, and if it’s archived, there should be a list of dates — keep trying until you find the site.
If you know any other ways, feel free to comment.