You can do it easily with Apache's mod_rewrite module: it's a mechanism that allows you to specify what content to serve for an incoming request. For example, you could make a rule, in your .htaccess file, like this:
RewriteRule (.*) index.php?req=$1
which would then redirect every incoming request to a central index.php, where you could parse the requested URI (in your example, the req variable would hold the value "zuck"), then you could serve some content based on that information (e.g. you could look up "zuck" in a database containing user profiles, grab the id associated with the "zuck" value, then show the profile for user #24).
At least that's the basic idea. It's usually called "URL prettifying" or "friendly URLs" or "SEO URLs", search around these terms and you'll find plenty of resources.