If you want to be able to install the SyntaxHighlighter in your wordpress blog, your best bet is to host it yourself (download the source from Wordpress.org). The free hosted version at Wordpress.com does not accept plugins, and does not offer the unlimited template customization that you might want to use when integrating SyntaxHighlighter.
You also might want to check out these questions (1, 2) on StackOverflow, as well as a blog post that I wrote on the subject.
If you really want to use the free hosting on WordPress.com, I would suggest using Windows Live Writer to post to your blog. It has a number of extensions that can handle code formatting (my favorite is Insert Code for WLW).
