There is no definitive answer to this question as it depends on the jurisdiction in which you reside. Generally speaking, however, blogging is not considered to be an illegal activity.
In some jurisdictions, such as the United States, blogging can be considered a form of free speech. Additionally, many governments see blogging as an effective way to promote civic engagement and community involvement.
While there may be some situations in which blogging can be considered illegal, such as when it constitutes defamation or slander, for the most part, blogging is generally legal. That said, it is always important to consult with an attorney if you have any questions about whether or not your blog activity is legal in your jurisdiction.