I own my domain, and to be honest, I'm a little snobbish about it. I just prefer a clean url over yourtitlehere.blogspot.com or titlehere.typepad.com. It's relatively inexpensive. I use wordpress too. :)
When I started doing paid blog posts and started posting in a frequent manner I bought my own domain. Luckily my previous free blog site through wordpress didn't have that big of a reader base and I hadn't yet been publicizing it as much on social sites so the transition was fairly easy. I do though have a link on my current self-hosted blog to my old site with previous posts.
The cost of my self-hosted site has actually been paid for through my paid posts so far. I did have to pay $15 for my domain year for the year and then if I were to pay my hosting site out of pocket it's 4.95 a month and well worth it to me. Mine is through Gatorhost.
I've been told that having your self-hosted site helps you gain more review/job opportunities bc companies see you as taking your blogging seriously.
I started with a blog on blogger.com and then had my developer work it into my site. How he did this, I have no idea. In fact, I am in the process of getting a "blog tutor" because I can't figure out alot of things like spam and sociable plug-ins and posting link buttons.