A key point about fires in space is the zero gravity. Without gravity, a fire can only be sustained if something is driving oxygen into the fire.
In the Russian space station they use CO2 as a fire extinguisher. The Russians claim that by using CO2, they are using a readily available substance that is already removed by the CO2 scrubbers in the air system. By comparison, Halon or Freon systems, while having the advantage of being inert, are hard gasses to remove from the air system. In a closed place like a space station, that is important.
A google search (www.google.com) found the NASA website search.spacelink.nasa.gov where you can search all of NASA's information. Typing in "fire suppression" brought up many pages of information including one on smoke detection and fire suppression. According to this site the fire suppression system on the space shuttle is based on Freon-1301 (bromotrifluoromethane) and Halon-1301 (monobromotrifluoromethane).