Advantages of a Custom Domain

Claim Ownership
Prevents someone else from owning your blog's name
Your blog will have a professional URL like or
Pro Email ID
You can use a professional email address like
You know you're a serious blogger. But your readers may not get that impression with a free blog domain like
Having a custom domain lets you change your blogging platform without having to change your blog's URL. (shifting from blogger to wordpress, for example)

Advantages of Self-Hosted Wordpress

Theme, Themes and more Themes
Use any of the thousands of Wordpress themes and customize it until it truly represents you and your content.
Choose from a plethora of plugins to enhance your blog. If you have a specific need, chances are - there's a plugin out there, waiting to do the job.
You can monetize your blog with complete freedom - and keep 100% of what you earn.
You'll have complete FTP access to your blog.
Unlike free hosting, you can use 3rd party analytics like Google Analytics to give you detailed stats.