OK, this may not be of interest to most people but I'm not that bothered at having the Google Searchbox up in my Navbar...

So, removing it is as simple as putting this into your CSS section of the blog design:

#topnavbar .gsearch {
display:none;
}

#topnavbar .gsubmit {
display:none;
}

#topnavbar #topnavSearch{
display:none;
}

#linkSearch fieldset {
display:none
}

Bingo, bye, bye Google, altough I'll admit this may not be for some!

Oh... and if you're as OCD as me the removal of your Google searchbar will make the bar look a little lopsided... so you can move your "Create new blog|flag blog" section over towards the left to centralise it a little more.

The code for that is:

#topnavbar #top_blogOptions {
position:absolute;
right:42%;
}

Or if you've used the background removal:

#topnavbar #top_blogOptions {
position:absolute;
right:42%;
background:none;
}

Just change the percentage until you're happy with positioning, I found 42% to be right, yours might be different.