An offsite established blog such as Google's blogspot or WordPress.com can benefit your site. Those types of sites overcome several of the challenges which arise when you try to set up a blog.
Advantages: quick and easy to set up, a unique C block for hosting, no worries about site maintenance, etc.
Disadvantages:
-
your blog content would not be on your site so would not benefit from the main site's DA. Also, your main site wont benefit from the links your content will hopefully generate. While you can link from your blog to the main site, it is not as beneficial as having a direct link to your site.
-
as Alan shared, your main site would also lose out on the freshness benefits a quality blog can offer
-
internal linking is also a fantastic means of properly directing the flow of PR throughout your site. With a single site, there is software which can automatically generate all your internal links as appropriate. For an external site, you would need to manually create all the links which is a lot more work.
Overall the best results should be achieved by integrating a blog into your existing site. You could choose an external blog and it can benefit your site, but not as much as an internal blog would.