1) To learn and to teach
To really be an expert in your field, it helps to be able to express yourself and explain your skills to others. Forcing yourself to explain a concept to someone encourages your to get a firmer grasp of it yourself. In fields like software development for instance, a key difference between intermediate and senior developers is the ability to concisely explains a concept in a meaningful and accurate way, to clients, fellow developers and managers.
2) To provide value
As an expert, or at least someone with some experience in a field, you help others on a similar path in life, or with similar interests. By reading your blog, other may painful mistakes you had to go through, and be able to reach their goals much sooner. While there are many ways to make profit on the internet, offering value of some kind is almost a prerequisite.
3) To document
By writing a blog, you will document a lot of the knowledge you may only have in your head. Doing so will force you to write it down, creating additional clarity for yourself and others. The blog not only helps others then, but serves as an organized repository of information that allows you to track your goals and keep a record of your own thoughts.
4) To make money
Making money, especially residual and passive income can be a key motivator for writing a blog. Some of my favourite financial blogs, such as mymoneymustache.com or financialsamurai.com net their owners hundreds of thousands a year. Both sites are well established, and the owners still make a lot of income even when they don't put a lot of work into the site. Blogging is pretty much the ultimate business, as capital costs are minimal, and one can work from anywhere. That said, like any business, it requires discipline, and success is not guaranteed.
5) To leave a legacy
Like any business, a blog is something you may wish to pass onto your children. Depending on its success, it may be carried forward by your family, leaving something yourself behind upon your death. If you don't achieve any success with it, keeping it operational after your death may be difficult, as keeping websites up in perpetuity without an owner is a problem yet to be solved, though I'm sure will be solved in the near Future
6) To foster discipline
Having some sort of accountability to someone, even if it's just a few readers over the internet, encourages you to be a more consistant writer. Moreover, if you track any kind of goals on your blog, be it the loss of weight, elimination of debt, or your net worth, sharing it with others will force you to stick to your goals more readily
7) To build a presence online
Even if your financial success due to your blog is limited, you will increase your presence online. You can showcase your work and your knowledge, and thus be more likely to land freelance gigs, find a new job, consulting work or speaking gigs, or whatever floats your boat.