I stumbled upon this feature in Word 2007 this morning. It seems that Microsoft and Google have agreed to play nicely for a change.
Posting from word is relatively easy - you select Blogger from the list of supported blog providers and give it your login details. Now you just type your post and hit the 'Publish' button and it will appear.
There are other options for blog providers, including Live Spaces, WordPress and SharePoint and also support for MetaWebLog and Atom APIs
Ideally I would have liked to give some screen grabs to demonstrate this but what I have found is that there is no easy way to get pictures to your blog. If you use Blogger though, you aren't able to upload pictures with your post.
It seems possible to use a third-party host such as PhotoBucket insofar as there are configuration options there to set the upload URLs but after much playing around, I haven't been able to get them working, mostly due to the fact that these sites don't allow for FTP uploading without a premium account.
Even manually uploading and getting a URL for the picture isn't helpful as Word doesn't seem to want to let you insert the picture from a weblink.
I guess I'll keep on playing with it...