I wish I knew this before I spent $12 on a custom domain for blog.zoopcast.com. You can’t use Google Analytics on a WordPress.com site.
I think the advantages of hosting the blog on their infrastructure outweigh the inconvenience of not having all metrics in one place (at least at this early stage), but it sure is an inconvenience.
Hopefully the WordPress.com Stats feature is good enough. From what I’ve read on TechCrunch though (and this is what sparked that whole “RSS is dead” fight last week), the stats that WordPress.com gathers don’t always match up with Google Analytics.