The internet archive is pretty much it, with Google being the "recent". Both of these don't work very well with pages that have scripting on them. Some will "refresh" even in the archive, and present you with the recent page.
You may not be seing anything past 2006 for whatever site you're looking for, because the owner has disabled archiving (via a robots.txt file, or some other method to keep "robots" from indexing web pages. It stops Google too).