How do I add google tracking code to a wordpress.com site?

the <script> tag is not allowed on WordPress.com

Since the Google Analytics script uses that tag, it’s not possible to add it. This has been asked and dealt countless of times on the forums of WordPress.com but they do not wish to compromise the security of their site by allowing scripts (Javascript/VBScript).

If you find a place to host your site and decide to use the WordPress app (found at WordPress.org), then you’ll be able to modify it and add scripts as much as you want! That’s what I ended up doing with my blog that I had originally created on WordPress.com.

Just as an extra, I found this interesting exerpt on their forums:

Google’s rule is that only one Google
analytics script (Urchin) can be run
on any blog; they do not allow two.
And wordpress.com runs Google
analytics (urchin) on all of our
blogs.

source: http://en.forums.wordpress.com/topic/google-analytics-on-wordpress-how_