I sometimes receive a request from my customers to completely remove the first tab from the Top Nav.

SharePoint 2010 uses UL's and LI's for its navigation and this makes it a little bit harder to hide just one element. However, it is possible to do by modifying some settings of one of the CSS classes that handles the Top Nav.

To do so, open your copy of Microsoft's corev4.css file, locate the .s4-tn li.static class and set it to this:

.s4-tn li.static > a
{
    display: none !important;
{
.s4-tn li.static > ul a
{
    display: block !important;
}

Don't forget to check in (and publish, if appliable) your CSS file, then go to the browser and test it.