Go to the UPM -> Manage add ons, and look for the system add-on that provides project blueprints/templates. Most of the project types are modules, so you can disable the individual modules and they'll vanish from the list.
In JIRA v7.0, go to JIRA Administration > Add-ons > Manage Add-ons > change filter to System and then find "JIRA Core Project Templates Plugin". Expand that list of modules and you'll find a lot of the project templates to disable. There's still one or two though I haven't found out how to disable yet.
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