There are many positive things about wordpress.com. With the new changes facebook did for the plug-ins, it seems that only wordpress.org or the blogs that are self host, are taking advantage of them. The like box that comes in XFBML and iframe format are not compatible with wordpress.com. The closest i was able to create, and still helps to generate traffic from your blog or site to your fan page, is the badge you see on the right side of my widgets. I will guide you to the steps to create  and insert in your widget section of your blog.

1. Be sure you are sign in to your facebook
2. Click this link https://www.facebook.com/badges/page.php
3.          it says “choose where to add the badge”- select OTHER
4.          copy the link that is generated
5. go to your blog to the widget section
6. drag the TEXT to the right widget section
7. paste the link generated by facebook
8. save it
9. And let me know if it worked.