I am going to answer this question as if you are using WordPress as your blogging platform of choice, because I use it myself and I have seen results from the tag system of using it.
Is it important?
It depends. Do you want to sit there and tag your blog articles as you write them? If your site already has a lot of traffic, then maybe not so much? If you want a lot of new traffic, and to grow even further, yes. It depends on how you view it and what your site is about.
Is it important for SEO?
From my experiences of having a blog, without using tags for a year, I noticed small growth with my site. I had to advertise and give out direct links to get people to join.
Once I added tags and did some SEO work on my site, I noticed a lot more search engine traffic coming to view my articles and posts. I am going to say yes to this question of yours, it can be important for SEO.