One of the long awaited features in Blogger Beta was the ability to restrict access to your blog. Designating your blog as private, to be read by authorised parties only, was a much requested feature.
Blogger Beta uses your Google account to identify you, and verify that you are authorised to view any blog (including yours). And that causes occasional concern, fortunately unnecessary in this case. Seeing your Google account, which coincidentally may be the same as your email address, as you peruse your blog, is a bit scary.
Rest assured, though, as you see your email address in your Navbar, every visitor to your blog is seeing their own email address in their Navbar. Nobody else sees your email address.
And if you're seeing an increase in spam recently, rest assured that it's not related to your Blogger Beta account, or your Google account, being visible to spammers.
None of this, unless your computer has become part of a botnet, is related to anything that you have or haven't done.
Relax just a bit. Concentrate on other, more urgent, issues - like the coming Beta migration. But accept the inevitable - you will need a Google account to use Blogger.
Your (Blogger) Google account, and your (GMail) Google account don't have to be the same, though. Google accounts are free, and you can set up another, if you like.
(Note 2/13): As noted by Pete in his separate comment, your email address is kept private, by carefully designed code:
The iframe separation keeps arbitrary Blog*Spot blogs from reading (for example) your Google Account e-mail address when you're logged in.