Adding a drop down field to user registration
It sounds like you've found where you can add user fields (under Administration >> Configuration >> People >> Account settings). Once you've clicked the + Add Field button, you can select List (text), add your Label, and click the Save and Continue button to configure the options you can add to your country select list.

Here is where you add your list of items. The Allowed values list text field is where you can add your selectable items. You can add each country you want, once per line. Once finished, you can click the Save field settings to continue to the final configuration page. 

Customize the remaining settings and click the Save setting button to finish adding the country select box for your user account.