With any website it's important to know how many visitors it is receiving. In the context of a blog knowing you're getting a lot of traffic can motivate you to publish more content and knowing more about your visitors can also feed into what sort of content you publish. You could look at your server logs, of course, but analytics is easier to set up and gives you higher quality data than something like AWStats. Since Google lets you opt out of sharing your data with them I don't see much argument against using it.