Script Summary: Use this GreaseMonkey script to reclaim the hefty area that the GMail's searchbar and Logo area take up.
This script hides that whole searchbar area by default, and provides a 'Toggle Search' link in the header to show/hide the searchbar area.
This script works for plain GMail as well as Google Apps hosted corporate Gmail too.
Another nice feature is that, that when showing the search-box, the focus is automatically given to the search box, so you can simply start typing your search query.
A video of the script in action:
This script has been adapted from the fine script at http://userscripts.org/scripts/show/43528 ; but it has gone through 5 revisions and quite extensive research to improve the functioning.