Refer to Simple adjustable way to hide Navbar for an easier way to hide the Navbar. Also see earlier update at the bottom of the post.
The navbar is compulsory for bloggers using blogspot.com for their blogs, and it can also be useful. It has a search box which will allow visitors to search the content of your blog. You can also change the color of the navbar to blend with the colors of your blog by going to the LAYOUT and right at the top, you will see a section for navbar. Click EDIT and chose the color for the navbar.
However, many people have expressed the desire to remove the navbar as there is "Next Blog" in the navbar which when click will lead to an unpredictable blog which may contain sexually explicit content, etc and about which people like educators who set up blogs for their students are very unhappy about.
Update 29 July 2007: Accoring to Kawaljit of Maybe it is OK to remove Blogger navbar, Google did a series of road show in some Indian cities to promote their Blogger platform. Ankit attended the event and asked for clarification on the navbar policy from the Google representatives at the roadshow. They called up their office in Bangalore office and confirmed that it's legal to hide the navbar.
If you really want to hide the navbar, this is how to go about it. Whenever you make changes to the template, it is always wise to backup the template first. If you are not familiar with that, refer to this post: Backing up and changing New Blogger template.
Sign into Dashboard, click LAYOUT for the relevant blog and then click the EDIT HTML sub-tab. This will open the template editor window. Look for this tag: </head>. Paste this script immediately above that tag:
so that what you see will be
Preview, and if satisfied, click "Save Template".
To demonstrate, I will hide the navbar from this blog DIY (Do It Yourself) which is a blogspot blog.
There are New Blogger templates by Final Sense which you get via links in New Blogger 3 column templates by Final Sense. Although there is a navbar Page Element in the Layout of the most blog templates, there are no navbar for blogs using Final Sense Color templates. So if you don't want a navbar, but have an excuse for it perhaps you may want to consider using Final Sense templates.
Update 5 July 2007: A blogger commented this method don't seem to work anymore. I tested before I published and it work, but on getting him comment, I tested again and found that what he said was true. I have tested a slightly different way of doing it at Another way of hiding the navbar and found that the alternative way worked. So if you still want to hide the navbar, refer to the new post.
Amazon products for Blogger
Another way of hiding the navbar (February 2007)
How to hide New Blogger Navbar (October 2008)
Simple adjustable way to hide Navbar (January 2010)