No Custom Templates Available

I’ve got three separate WP installs on three totally unrelated hosts with three different themes, all updated to 3.2.1. Today I decided to add some custom page templates to one. And for the first time, I realized there’s no dropdown boxes on the post page to select a custom template. I checked my other two installs and it’s the same there, too. No way to select a custom page template.

I’ve searched here and found reports of this happening with others. Those solutions have not worked for me. In fact, I just did a clean install, with no plugins. No way to select custom page template.

Any suggestions? Am I missing something new with 3.2 or 3.2.1?