A number of users who are using Norton Internet Security 2008, have reported getting certificate errors when navigating to Web Mail. The error will inform you that "Revocation information for the security certificate for this site is not available".
When using Norton 2008, the problem can also happen on other web sites, not just EarthLink Web Mail. Norton has published a support bulletin on their site here. The instructions say that running Norton Live Update will fix the issue.
A similar problem happened last year with Norton 360, and Norton fixed it with an update to their product. So perform the update function built-in to the Norton software and see if that resolves it. A Google search shows me that it is happening to users of Norton 2008 on other web sites, not just here.
But Web Mail is safe to use. The same certificate check is built in to the IE7 browser (Tools / Internet Options / Advanced / Check for publisher's certificate revocation) and if you allow IE to do the check without Norton running, it will pass and not give a security warning.
Again, Norton's instructions to fix the problem are here.
UPDATE: based on a report from user David Schwartz below, there apparently are two separate problems going on here. If you use IE6 without Norton, this problem can occur if you have changed the advanced security settings in the browser. But if you use IE7 (which has that setting enabled by default), the problem only occurs if you do have Norton (not updated). We're working on the IE6 issue now to find and fix the cause if it is on the EarthLink side. Thanks for the report.
UPDATE: the IE6 problem is fixed.