store country name or country id
It's better to have a separate table. That way your data will be normalized.

In your specific case you most likely want a list of countries the user can select from (eg. it's not a free form field). By having it be a separate table and referencing the country id you can setup a foreign key constraint to your countries table. This way your data will always be in sync as user's will not be able to enter a country that does not exist.