Not exactly a time machine, but yes this website let's you visit the old archives of a "particular website".
All you have to do is enter the URL and go turn on your reminiscence mode on!
Here are the screen captures of different websites from 2006-2007(I love that year):
Facebook:
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Google:
Yahoo:
Wikipedia:
Reddit:
YouTube:
Orkut:
The Time Machine itself:
Tool used: Waybackmachine
