Which bacteria can fix atmospheric nitrogen?

A bacteria that can survive in an area without fixed nitrogen is called a Diazotroph. These organisms use an enzyme called nitrogenase to fix their own nitrogen into the soil. Most have a symbiotic relationship with a plant, forming nodules in the roots of their partners. 
The most studied nitrogen fixing bacteria are Klebsiella pneumoniae and Azotobacter vinelandii. The Klebsiella is an anaerobic bacteria, meaning it is adverse to oxygen, while the Azotobacter is aerobic, meaning it needs oxygen to survive.
Rhizobacteria grow in the rhizomes of symbiotic plants like those found in the legume family. These nodules grow on the roots of the plants.
Some cyanobacteria can fix nitrogen, and are known for fertilizing rice patties.
Most nitrogen is fixed in the form of ammonia (NH3), nitrites (NO−2) or nitrates (NO−3).