https://web.archive.org/web/2oe_/http://wayback-fakeurl.archive.org/yt/<videoID>
replace the brackets containing videoID with the string of letters identifying the youtube video you want.
edit: as you might guess by looking at the url, this only works if the video has been archived by wayback machine.
found it useful, maybe you will too
I got a 404, so I tried it without yt/ at the end and got a message from the wayback site that "that page has not been archived yet." https://web.archive.org/web/20130720113437oe_/http://wayback-fakeurl.archive.org/
??