How do I output a dropdown's values if I'm on a registration form not tied to an entry?
The not so elegant way to do this is to re-use the field somewhere else, where you do have access to (e.g. a global set). But you probably want to avoid this, right?

What you can do instead is to access the field directly using craft.fields. This function returns the FieldModel of your field, containing all of its properties. The FieldModel property you want is attributes.settings, where you can access your dropdown options like this:

{% set dropdownField = craft.fields.getFieldbyHandle('dropdownFieldHandle') %}

{% for option in dropdownField.settings.options %}
    {{ option.value }}
{% endfor %}