I blog for a company and I have my own blog. I think ultimately for any company blog that it would be SEO in my opinion. Let's face it, everyone is keeping up with social media to ultimately build more revenue.
As far as my personal blog I use it to help other breast cancer survivors and support breast cancer awareness.
(Business Development, Pinkerton Consulting and Investigations)
Definitely Authority and SEO.
Community is really a tough nut. You can't expect the 'if you build it they will come' mentality. The diversity of channels (via social media, RSS, email) means that each audience member can enjoy your content when and how they prefer. A real community would require comments and interaction. These days, thanks to Facebook we are happy if someone clicks the 'like' button.
I would have to say that being an authority and for SEO purposes. When you are sharing thoughts or ideas about something on a blog, it's to help give you credibility for what you're saying. people will always research what's being said if they're not a sheep who's easily led and believes everything. It's important for companies to have a blog as a good way to get customer feedback quickly. When someone is passionate about something, they have a right to say what they want. Again, this goes back to credibility and researching what's being talked about.
This is also the same for those who are a part of internet marketing, including myself in this one, who have ideas for products and do part time consulting for small business. When I blog about something, I want to make sure that everyone can easily understand what I am saying and show that I can rationally talk about how a business or individual can make money or increase their web presence to their benefit. By doing so, it helps them and it helps me the same way.
When talking about SEO, everybody knows that if you talk about the right keywords and promote the right items or backlink everything to your site, it can potentially increase your audience and boost your possible revenue from sales. This is important for any business, no matter what size. When a customer is looking for a product, they will use they keywords necessary to find that product. The same can be said about those who blog. If they are looking for a particular blog or subject in a blog, they will use whatever keywords are necessary to find it.