A friend of mine recently moved his blog off of Blogger's blogspot domain and onto his own domain. Unfortunately, he's paid a stiff price for that move, because he can't change all the inbound links to the old blog address. As a result, his traffic to his blog has dropped sharply, as has his AdSense income.
This is why in my book I tell Stef to register a domain and find a web hosting company to host the domain. Even though she's using Blogger to actually run the blog, she can configure Blogger to publish the blog on her site, not on its own domain. Yes, the blogspot domain is convenient to use, but it's not without cost.
Now, some people will argue with me that any change to a blog address is bad. And, yes, I'd say it's best to keep the same exact URL for a blog whenever possible. So choose wisely when you start. Sometimes you have to change, though, and if you own the domain then at least you can do things like redirect visitors from the old address to the new address. You have more control, it's as simple as that. And if you're making money from that blog, don't you want as much control as possible?
Eric Giguere is the author of Make Easy Money with Google: Using the AdSense Advertising Program.