Here are a few non-governmental conservation organizations.  They are primarily wildlife-oriented because they are what I'm most familiar with.  

Environmental Organization Web Directory

General Environmental Conservations Groups

Union of Concerned Scientists (UCS) is a non-profit alliance of scientists and citizens working for a healthy environment and a safe world, UCS researches and promotes clean energy and transportation technologies.

The Nature Conservancy :The mission of The Nature Conservancy is to preserve the plants, animals and natural communities that represent the diversity of life on Earth by protecting the lands and waters they need to survive.

Project WILD is one of the most widely-used conservation and environmental education programs among educators of students in kindergarten through high school. 

Sierra Club   

   

Wildlife Conservation Groups

Izzak Walton League of America  was founded in 1922 as a national organization of hunters, anglers and other conservation-minded outdoor enthusiasts who work through volunteer, community-based action and education programs to ensure the sustainable use of America’s natural resources. 

The National Wildlife Federation is the nation's largest member-supported conservation group, uniting individuals, organizations, businesses and government to protect wildlife, wild places, and the environment.

The Wildlife Society, founded in 1937, is an international non-profit scientific and educational association dedicated to excellence in wildlife stewardship through science and education.

Wildlife Management Institute  is committed to the conservation, enhancement and professional management of North America's wildlife and other natural resources.

The Theodore Roosevelt Conservation Alliance is a conservation association of fish, wildlife and habitat stakeholders who will motivate hunters and anglers to positively influence the future of our 192 million-acre National Forest system.

Hornocker Wildlife Institute has followed the wisdom of the great conservationist Leopold by using hands-on field research to understand our place and responsibility in the natural world's fragile ecological structures. 

Wildlife Forever conserves America's wildlife heritage through preservation of habitat, conservation education, and management of fish and wildlife.

Groups dedicated to a species.

The Cradle of Forestry in America commemorates the first forestry school in America, set in the mountains of North Carolina.

Tall Timbers Research Station looks at fire ecology and related topics.

The history of the Boone and Crockett Club is a chronicle of over 100 years of measured and thoughtful commitment to conservation. It is a commitment that balances human needs with wildlife needs; a commitment that sees deep value in preserving the hunting tradition, as well as conserving wild lands and wildlife; a commitment that grows out of a powerful love of wildlife.

The Extirpated Species Foundation assists in efforts to repatriate locally extinct species of indigenous animals and plants for the enjoyment of future generations.  Efforts are concentrated in the highland areas of the southeastern US. 

Wildlife Habitat Council is a nonprofit, nonlobbying group of corporations, conservation organizations, and individuals dedicated to protecting and enhancing wildlife habitat. 

Since its official inception in 1989, CAMPFIRE has engaged more than a quarter of a million people in the practice of managing wildlife and reaping the benefits of using Zimbabwe's wild lands.  The site includes a number of fact sheets, including one on  hunting.