Do you own your email address? How about your web address? These things, like your telephone number, identify you and need to be something you have control over. How you do that is by owning a domain name. If your email address ends in comcast.com, bellsouth.net, msn.com, or aol.com or something similar then you don't own that part of your identity and you don't have as much control over it as you would believe. The same applies if your blog ends in blogspot.com, wordpress.com, or typepad.com. The companies providing your email or hosting service could go out of business tomorrow, raise your rates to exorbitant levels, or unilaterally decide to cancel your account. Anil Dash covered this years ago, and it's truer today than it ever was.

To own your email address, or your web address, you need to own a domain name. On the internet a domain name gives you the equivalent of number portability, except, unlike the telephone number portability, this one actually works. What a domain does is give you control over who provides your services. You, as the domain owner, get to decide who provides your email services, web services, chat services, etc. And the way DNS works, you don't have to use the same provider for each service. For example, I own bitworking.org, and I use Google Apps as my email and chat provider, and Webfaction as my web hosting provider. I could easily switch email or web hosting providers by merely updating my DNS records and you, either as a blog reader, or email sender, or chatter, would never know the difference. As a matter of fact I just recently did this, moving both my email and hosting providers. Did you notice? I hope not.

The nice part about owning a domain name is the utility. You don't just get email portability, but all the services that you can hang off of a domain name are subject to the same level of redirection. Email, web, and chat are all able to be hosted in different places using different 'records' in the DNS registry. When you set up your blog you point the A or CNAME record at the server where your blog is hosted, you set the MX records to point at your email provider, and you add a mix of A records and SRV records to point to your chat provider.

Now while I've known this for years and owned bitworking.org for myself I only recently realized that I was living the cobblers-children-have-no-shoes metaphor and so set about getting Lynne set up with her own domain name, zen5.me. To my mind the easiest way to get set up is to get set up with Google Apps. You buy a domain name in the process, or can use one you already own, and it includes both email and chat. Note that it doesn't include a blogging option, but you can always set up a Blogger blog as a sub-domain of your Google Apps domain. And, most importantly, if you want to switch service providers for any of the services you are free to do so, because you own the domain name.

Notes

chat
I use the term chat, but really the underlying protocol is XMPP, formerly referred to as Jabber, but calling it your XMPP provider would be the same as calling your email provider your SMTP/POP/IMAP provider; while true, it's just not true in any way that helps the conversation.
data portability
Now you may rightly point out that switching DNS records to point to a new service provider is half the battle and that actually moving your data to the new service provider may be a larger battle. I can't speak for everyone, but Google does have an internal group, the Data Liberation Front, that works on exactly that problem.
ownership
Yes, you actually rent a domain name and not own it, and yes they can be stolen, but that's a completely different topic.