Are you entering this code as the title or as the description? Titles do not allow anchor tags in them and will be stripped out. Anchor tags work fine in descriptions however.

I am entering it in the description box. I am beginning to think there may be something wrong with my installation, as I cannot click on the tags tab either.

Yep, there's definitely something wrong with your installation. Did you upgrade a previous version of zenphoto, or is this a fresh install. Have you changed the permissions on any part of the filesystem? Some specifics in regard to your server setup would help in troubleshooting the problem.

I have reinstalled zenphoto, and now I can tag things, but still can't put links in image descriptions. My server setup is a basic account at hostgator, where I have a user with all permissions as the admin user on the zenphoto database. Is there a way to stop zenphoto from stripping HTML. I'm not opposed to editing the source, but I don't know where to look. Thanks for the help so far.

This has been fixed in build 2231.