Yes.
Of course, the real caveat is what you hope to accomplish with your blog. Also, you could design your own site. Depending on your geek level, it could be possible, if time consuming. Also, would you host your blog on your own domain or with a site such as wordpress or blogspot? What kind of template would you use? What kind of marketing do you plan on doing? What are your publishing credentials?
These are not questions you need to answer to us - it's more to get you thinking about what it is that you expect a blog to accomplish for you.
Another question is how much you think it's going to cost. If you design your own, then costs are limited to domain registration once a year (about $8 or 9) plus domain hosting (say, $3-10, depending on features you get), so costs can be fairly low. Templates, depending on what you're using for either a CMS (content management system) or for the blog can be free and you can customize, and a lot of software can also be had for free. But it also depends on what you want out of the software and what your expectations are.
Personally, I'm all for doing things on the cheap and, other than domain hosting and domain registration, I pay nothing. OTOH, I also have a geek husband who helps out, plus I'm fairly geeky in my own way.