Because blogging is a community activity, bloggers regularly link to and comment on the content of other blogs. Since their post, comments and content are highly related to the blog that they're referencing, you have another trait that is treated well by the search engines. Relevant one-way links help immensely with SEO.
Should you keep SEO top-of-mind when you're writing your posts? That's not necessary, but do use a few simple techniques when you're writing for your blog.
1. First and foremost, write for your readers and post content that will be of interest to them. Just doing that will accomplish more than you might think. I have a blog about Taos, NM Real Estate. Some of the search terms that have been used recently to bring visitors and my blog's position in the results are "real estate""time on market"southwest(Position 4), taos nm well depth(Position 1), taos nm realty map(Positions 3&4), and sold land prices in taos(Position 1). None of these clicks were paid for. They all brought visitors because there were posts that mentioned or talked about the subjects of the search.
2. Once you've built up a good bit of post content in your archives, place a link in your post to other posts that are related and still current. Do it only if the other post is relevant and adds to the value of the current post.
3. Participate in the real estate blogging community. Read other real estate blogs. Read industry related blogs about mortgages, trends, etc. Comment on other blogs' posts. Writing posts in your blog with reference links to others will build good will and get you some exposure in return.

