What is the Blogger navbar?
Blogger navbar is the *navbar* you see at the top of your blog, and which allows users to move to a next random blog. It allows user to search your blog and also to mark any blog as spam.

So why should I remove it?
It depends on your perception. I find it unprofessional, because it sometimes spoils the look of your blog. If you have a subtle layout, they might get too obvious.

Are there any problems if I remove it?
Some of your viewers might be accustomed to a navbar and may miss it. Blogger calls navbar the bloggers equivalent of remote, as it allows bloggers to switch from one blog to other.

Ok how do I remove it?
If you are using Blogger for any length of time, you must be knowing how to edit the templates. So in your template find a >style type="text/css"> tag. Just after that insert
#b-navbar {
height:0px;
visibility:hidden;
display:none
}

Thats it. Save and republish. Your navbar should be gone.

This trick was first published at blogger-templates.blogspot.com

But does this not violate my Blogger TOS?
Blogger makes no explicit term that you may not remove it. But they do not also say if you can remove it. Also this is a pretty standard trick. So doing this should be no problem.