I can't get any content module to work. They all seem to install ok, but when I click on Add Content or similar (depending on the module), it just dumps me back on the module options page.
If I try and access the module through the main menu item, it keeps adding ?id= to the URL, ad infinitum.

I'm using XOOPS 2.0.16, and the most recent versions of the content modules I can find.
Every other module I've installed works fine.

Is there something I'm missing?

Assuming you mean 'static' HTML content, try 'Content 0.6' from here in the repository. Be sure to read my post in the comments which leads to a small bug-fix.

I believe (but cannot confirm) that this works fine with XOOPS 2.0.16.