Personally, I think blogs are a fantastic opportunity for us music types, and not just because I'm writing a blog post now! A blog is a way to communicate with friends, fans and contacts in the industry, including a blog on your website, or even replacing your website with a blog is a way of turning a static, brochure style site into a living, breathing online representation of yourself, and your work.
How to approach your blog.
Successful blogs, musical or otherwise, always manage to strike a chord with their readership. Base your posts on what type of band/artist you are, if you're a band who deals with political and sociological issues, write about current events, give your opinion, stir things up a little. If you're an electronica artist, post about your studio, your gear and your techniques. Of course, talking about other musicians can help you too, and linking to their sites or blogs - build a few alliances and you'll be well away. Talking about relevant subjects that don't revolve about how good your latest track is or when it will be released or how people can buy it can not only keep your fans interested in what you're saying, but can even drive traffic from google, or, if you get people talking, provide some word-of-mouth marketing.
Post regularly but not too often, a couple of posts a week is enough to keep people satisfied without overloading them.
Communicate! Blogs, like everything else you do online, should be another way of communicating with people. Industry professionals, fans, even friends. Make sure you encourage people to participate, and respond to all the comments and emails you get, people will think a lot of you.
Be constructive with your blogs, and you'll reap the rewards.