UPDATE: See the comments on this post that may make this post irrelevant 🙂
A minimal Joomla! 1.5 install without any sample data seems to not show core modules such as mod_syndicate. It turns out that this is so by design. This excellent post shows how to enable these extensions.
Essentially, the module XML file does not list all the files that are part of the module. These need to be added to the XML file and then the module files can be zipped up and installed through the administrator. You do need to remove the corresponding folder from the server before attempting to install it.