Wayback Machine which shows archived versions of websites on Internet Archive has got a Chrome extension. This extension after installing when detects dead pages -that returns page not found or 404 error- in Chrome browser, silently quires the Wayback Machine in real-time to see if a copy of page is available, if available, a notice is displayed in browser to see the archived page.
Wayback Machine Extension for Chrome
Do know the page of website you’ve encountered not found, should be stored in archive site, then only Wayback extensoin can able to display the notice, so that you can then able to see the page. Finding cached version of the page on Google in Chrome is another option you can try.
You can download Wayback Machine extension from here.