On the Statistics page there is a count of Visitors to the site within a 24 hour period. Does this include only those registered on the site? Or does it also include "lurkers"?

It includes lurkers or anybody else from the public who loads your home page. If you want a good representation of what members are actually logging into the site, click the Last Logins link on your Statistics page.

Brad Switzer wrote:

Does the number under the Home Page Visitors* count members only when they actually load the home page, or does it include members who access the site through direct links to other pages (like a message thread or a bookmark to a forum)?

The 24 hour cookie is only counting visits to the home page, and is meant to provide an estimate of the number of unique visitors who are coming to your site. If you want to see more specific numbers for every page of your web site and overall hit counts, you should set up Google Analytics tracking under your Preferences link.