As more and more people are uploading their lives to the Internet, it's becoming more important to pay attention to privacy policies and how stable your hosting company is. If you're using free services like Blogger, Facebook, LinkedIn, Google Docs, etc. you're at the mercy of the company who is holding onto your data. If you're just using a hosting company, you're in charge of all your own data, but there's still not much you can do about it if they go down. Of course, they can always take you down if they receive a copyright violation notice from anyone.
Kaushal Sheth recently posted about his web hosting woes, when his host died one day. He's moved on to a more stable one, Host Monster. WestHost is a good one that looks to be good, stable, and a pretty good price.
Wherever you end up, prices are low enough that you want to shop around and really make sure you get the service you need. Look for the availability of server side scripting languages like PHP and databases like MySQL or PostgreSQL. Many hosts have free applications you can use for hosting your blog, but as long as they have a database and programming language support, you can always upload your own applications. You don't have to use their wiki or photo sharing program. Just find an open source one and upload it yourself.
I personally use mostly the free services provided by companies rather than put together my own fully integrated site, but that is mostly because my research is headed in that direction - using existing Web 2.0 tools to collaborate and integrate content with other people, since that's what the majority of web users, who are not necessarily programmers, are going to be doing.
Whatever direction you end up taking, create a backup plan. After you've lost your entire life's work, it's a little late.