At the root of your site (and I mean the *root*, not any subdirectories), create a robots.txt file.
In that file, put the following:
User-agent: ia_archiver
Disallow: /
This prevents archive.org from archiving your site.
To prevent Google from keeping a cache of your site (but still allow them to index it), add this to your theme's header.php (near all the other meta tags):
<meta name="ROBOTS" content="NOARCHIVE">
<meta name="GOOGLEBOT" content="NOARCHIVE">
To prevent many others from doing the same, add these as well:
<meta http-equiv="CACHE-CONTROL" content="NO-CACHE">
<meta http-equiv="PRAGMA" content="NO-CACHE">
There is no real way to prevent *all* sites from keeping archives of your site. But these methods above will keep almost all well-behaved systems from doing so.