Organizations that lack borders:
Doctors Without Borders
Reporters Without Borders
Teachers Without Borders
Engineers Without Borders
Clowns Without Borders
Lawyers Without Borders
Builders Without Borders
Sociologists Without Borders
Grantmakers Without Borders
Firemen Without Borders
Magicians Without Borders
Homeopaths Without Borders
Veterinarians Without Borders
Wrestlers Without Borders
Architects Without Borders
Diplomats Without Borders
Librarians Without Borders
Acupuncturists Without Borders
Geeks Without Borders
Naturopaths Without Borders
Translators Without Borders
Musicians Without Borders
Demographers Without Borders
Ones that miss the target on naming conventions:
Basketball Without Borders
Ministries Without Borders
Friendships Without Borders
Bread Without Borders
Theatre Without Borders
Schools Without Borders
Honorable mention:
Greek Ecologists Without Borders (only having ecologists who are Greek seems a little odd - the idea of a lot of these organizations is to be international in nature)
Not found:
"Border Guards Without Borders"
"Border Collies and Border Terriers Without Borders"
"Border Conflicts Without Borders"