NGO

NGO stands for "non-governmental organization". These independent entities are often international in scope and shepherding thousands of employees, focus on world problems such as poverty, health care or women's rights. Unlike corporations, NGOs are not-profit. Real NGOs that are well known include the Red Cross, Oxfam, Doctors Without Borders and Amnesty International.

In fiction, these organizations may be fictionalized versions of real NGOs, or entirely new organizations that might take on real or fantastic threats. That as say, an NGO that focuses on the threat of robot invasions. Such non-state actors tend to be supported by rich benefactors, either eccentric philanthropists or a shadowy council.

If they're not really that non-governmental, they're called "quango" in the United Kingdom, short for "quasi-NGO".

Compare/contrast NGO Superpower. Due to it's profit motive, Mega Corp generally isn't counted as a true NGO despite its non-governmental nature.

Examples of NGOs include:

Anime and Manga

Tower of God: The Walhaiksong, founded by Urek Mazino, is an organization that seeks to leave the Tower instead of climbing or residing in it and has as much influence as the Ten Great Families.
Solomon, including the STNJ, from Witch Hunter Robin, with shades of Church Militant.
Nergal Heavy Industries in Martian Successor Nadesico, straddling the line between this and Mega Corp.
Celestial Being in Mobile Suit Gundam 00.
Terminal in Gundam Seed Destiny.
Several characters in Negima mention that most mages on Earth work with various NGO's across the planet.

Film

District 9: Multinational United likes to think of themselves as this. However, they are more of a Mega Corp
SPECTRE from the James Bond flims. They're a terrorist organization, who ironically use beneficent NGOs as covers.
The Men in Black become this after cutting off ties with the United States government. According to Kay, they ask too many questions.

Literature

The Encyclopedia Foundation in the Foundation series. It starts off as an NGO devoted to preserving all the knowledge in the universe. However, it turns out to be a ruse.
- The Foundation presented itself as this during "the Four Kingdoms" peroid, claiming to be a religious order that helps any nation with it's needs. The reality was that the Scientific faith was just a tool of the Mayor to help protect the Foundation.
The Wilmarth Foundation in the Cthulhu Mythos, which attempts to deal with the Great Old Ones.
The Howard Foundation in Robert A. Heinlein's Future History, whose purpose of extending human lifespans through selective breeding.

Live-Action TV

OmniFam from Alias
In one episode of City of Men, an unnamed NGOs gives Larajinha and Acerola a video camera.
International Rescue from Thunderbirds puppet-based TV show.
The Sanctuary network.
The Phoenix Foundation from MacGyver.
Foundation for Law and Government in Knight Rider.

Tabletop Games

The United Nations Tribunal for International Law, or UNTIL. In the Champions Universe, they're often the first line of defense when supervillains drop by for a visit.
The Aeon Society, latter Aeon Trinity in White Wolf's Trinity universe.

Video Games

BSAA from Resident Evil
Philanthropy from Metal Gear Solid
Vanguard, a special branch of the U.N. in City of Heroes. A joint task force of both heroes and villains, it's primary goal is to protect Earth from invasions by the Rikti and other extraterrestrial sources.

Web Original

SCP Foundation.

Western Animation

WOOHP (World Organization Of Human Protection) from Totally Spies!. Their background is however a bit unclear. They have connection with several governments but don't rely on them.
The Center in the Martin Mystery cartoon, also an MIB agency.
The Kids Next Door

Real Life

In Afghanistan, many NGOs provide aid and assistance to the Taliban and their allied insurgent groups. Sometimes the Taliban demands medical aid as a condition for the NGO to operate in their area, while other times the NGO actually supports Islamic jihad. When these groups are identified and targeted, their governments refuse to admit they colluded with the enemy to avoid being shamed.
The National Underwater and Marine Agency (NUMA), originally created by Clive Cussler for his NUMA Series novels featuring Dirk Pitt, then Defictionalized. The fictional version was the oceanic equivalent of the National Aeronautics and Space Administration (NASA). The Real Life version is an NGO and not likely run as it is portrayed in the novels.
The Wikimedia Foundation, which hosts Wikipedia as part of its mission "to empower and engage people around the world to collect and develop educational content under a free license or in the public domain, and to disseminate it effectively and globally", is an arguable Defictionalization of the Encyclopedia Foundation.