I'll agree with most of what's already been said. Email marketing and blogs are two separate fields, however, your website may be able to benefit from having a blog.
And as Kevin and Steve already mentioned, you can install a plugin which sends an email to your subscribers each time the blog is updated.
You can also mix and mingle - for a couple of my blogs, I blog the newsletter and that gets sent out as a notification email just like a traditional newsletter. Other blogs I don't use the plugin to notify of new entries, I use it as a mailing list manager to send out a 'weekly round up' of the previous week's posts.
As for the available plugins - there are a number of them. I know Expression Engine also comes with mailing list software built in.
If you're using WordPress, there are more than a few options available. I've personally used and tested a number of them and recorded my thoughts in an entry on finding
Each has their strength and weaknesses and it will depend on what you truly hope to achieve with your blog.
You also should consider that blogs can afford you a wider range of exposure through RSS and blog search engines/directories so you're not limited to just a few sources of new readers.
Just my 2 cents - hope it helps out
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