If you are using free blogging platforms like Blogger, Tumblr or Wordpress.com, you have no control over when these platforms decide to close you down.
As for the Google indexing point laid out by SpaceBOT, I would say that this is not true. Self hosted Wordpress blogs can do on page SEO optimization better for the search engines with some great SEO plugins like the All In One SEO Plugin. The speed of indexing depends largely on the number of authoritative links that a site is getting rather than what CMS are you using.
Setting up a self-hosted Wordpress blog is not that hard, even for a complete newbie as most web hosts come with a installation program called Fantastico which you are only required to type in some details and click Next Finish.