I think I’ve talked about this amazing tool before but it just came up for me again. The Wayback Machine (http://www.archive.org) keeps older versions of web sites. They don’t keep every web site, but they keep a lot. Also their funding seems precarious so some years they archive more than others. So say you want to find a web site that’s now defunct, visit the Wayback Machine, put in the address and cross your fingers. This works best for older, more popular sites.
If that doesn’t work, you can always try Google’s cache. Do a keyword search for the site in question. If Google has a record of it, it will come up. If the site is gone, clicking on it will not help – but you could try the Cached button found on the search results page, usually under the site description. This works best for newer (or more recently deceased) sites.