There is no definitive answer to this question as it will depend on your specific blog and the jurisdiction in which it operates. However, generally speaking, if you are blog writing for personal or commercial purposes, you will likely need to obtain a business license.
This is because most jurisdictions require bloggers to disclose their financial interests in their writings.
Some jurisdictions, like California, even go so far as to require bloggers to register with the state as a business entity. Failure to do so can lead to fines and other penalties.
So, while there is no one-size-fits-all answer to this question, it is important to consult with your local authorities if you are uncertain about whether or not you need a business license for your blog.