We humans need oxygen to survive. An unfortunate chemical fact of oxygen is that it sometimes has this reaction that we don't want wherein it violently combines with materials that contain hydrocarbons of some sort, a reaction we know as "fire." (They're more prevelent than you think. Wood is made of a complex matrix of carbon, hydrogen, nitrogen, and so on. Plastic is pure hydrocarbons. Think of how many things you own that contain some amount of either wood or plastic, or both.) Fire is bad for us. The heat damages us, the combustion products damage us, and if the temperature gets high enough, we can combust too. So it's best, if a fire does occur, to escape, and have insurance pay for all the stuff fire ruined.
In the early days, we found that water quickly smothered out fire. Partially because fire proved unable to extract the oxygen in fire, and also partially because water quickly absorbed much of the heat the fire needed to continue. This isn't always the practical way to fight it. Electrical fires don't react to water very well, and water in a grease fire, as may occur in a kitchen, will only make it worse as the burning grease manages to rise above the water's surface before it can be extinguished.
Later, work with computers produced carbon dioxide and halon exguishers that could end fire without damaging the water-sensitive electronics. Humans had to quickly evacuate, as any human near these would be suffocated in short order. Halon also proved bad for the environment after its release.
Firefighting experts tell us that fire is like a triangle. There are three factors for the continuation of a fire. If any one of them is removed, the fire stops. The three factors are: Fuel, Oxygen, and Heat. So you can fight fire by removing what would have burned, by smothering it under water, earth, or chemicals, or by chilling it. Most firefighting today works on the oxygen angle, as anything that displaces oxygen from the fire works.
Now, I can imagine a thermal-extinguisher that dropped well-insulated liquid nitrogen on fires, ending them, or some sort of brick-off machine that seals rooms that catch fire, perhaps from the top down to assist human escape, but I think the most important thing is to plan for fires. History tells me that Rome often caught fire, because it was made mostly of wood, was really crowded, and had a lot of people who could benefit from arson and didn't care who else was hurt by that. Rome would often burn down, because the fire department back then were bucket brigades, who could kind of ineffectually splash water on the blaze, which only slowed it down a bit. This was when they were not personally the arsonists! The modern world has way more burnable things...but also a fire hydrant once a block, fire departments who have all kinds of equipment, including hoses that spew water at ludicrious rates, chemical extinguishers, and tools to extract all humans from the area so that all kinds of chemical hell can be poured on the fire.
So to prepare, I think all areas that could conceivably catch fire have some sort of sprinkler, halon, or other firefighting system. If people leave the scenes of fire quickly, automated systems can rob the fire of oxygen with minimal damage to life and property. I'm also wondering about the safety of a liquid nitrogen based system.
Breaking news: It seems I wrote this article before. Whoops.