Yes, you can, but you have to be aware of the limitations. First of all, your content would be housed by the platform you choose. Although sites like WordPress.com and Blogger are probably not going away anytime soon, you could end up scrambling if they do decide to close down. Also, if you inadvertently break their terms or service, your content could be lost if your account is suspended.

You will also lose out on the ability to enhance the functionality of your blog on free platforms. Companies who build their blogs on their own domain using WordPress have unlimited options for adding opt-in forms to generate leads, customizing their template to integrate seamlessly into their branded website, enhance search optimization, and much, much more.

In terms of search, if you were to decide to move to your own domain after starting a blog on a free platform, you would ultimately lose the search value you gained from links to your blog content and the social shares you had received. While some free platforms allow you to redirect your blog to the new site (for a price), most do not.