By signing up with a free blog website, you may find it even easier to get your site listed in search engines like Google, Yahoo, and MSN, than you would if you were to start your own blog from scratch. For example, Google runs the free blog hosting site Blogger and crawls its pages regularly looking for new updates, so if you have your site hosted by Blogger you're almost guaranteed to be listed on Google. This easy access to search engines can take some of the work out of promoting your blog, it can also help you gain a lot of followers, and with very little marketing. Of course you must have good and unique content, don't think just because you have a Blogger account that you'll automatically get top rankings with Google, unfortunately it isn't that easy.
If your blog does attract a large group of readers, you should probably consider moving your blog site. A lot of people feel that free blog hosting for your blog site gives it more of an amateur feel to it, which is fine for bloggers that are just starting out, but isn't so appropriate for a more high profile blog site.
Starting your blog on a free blogging website is a great way to build a following before you spend any money on your blog. If and when your blog becomes popular and you're ready to take the next step and purchase your own domain, your readers will follow you to your new home. The fact that it's possible to use an awesome blog host like Blogger, or Wordpress as a start for your blog website is great news for bloggers everywhere in the world. I guess that's why so many people who have never had a website, blog, or any other kind of presence on the web before, find themselves suddenly drawn to blogging.
Also, having your own domain can help make your blog feel a little more professional, and finding a company that will host your domain is not hard or expensive. If you're lucky and your blog takes off, you just might be able to sell enough advertising space to afford to buy a domain and pay for a nice hosting package. However, it doesn't make too much sense in most cases to invest in these types of things before you have a large number of followers.