As it always has been, fire is a terrifying event and you certainly aren't to be afraid of it and take extreme measures to prevent it from happening. Of course, a controlled fire in a fireplace can add a nice ambiance to a room and a well placed candle can add romantic lighting or nice smells, but an uncontrolled fire such as from a dryer, electric short, or cooking stove is an entirely different concept.
Smoke Damage from a Small Fire
Even a small fire you're able to extinguish yourself can cause a lot of damage. Smoke can and will penetrate every nook and cranny it can reach, leaving soot, dirt, and grime. Paint and wall coverings will be discolored and likely require replacement. You'll probably need a professional cleaning service to get all the soot, as it will be in the furthest back corners of cabinetry and behind everything, even inside the electric boxes behind outlets and ceiling fixtures as well as having settled deeper in carpet than the typical vacuum cleaner can get. The worst part is the smell will remain until every last bit is removed.
Cosmetic Damage from a Medium Fire
A medium sized fire can cause much more extensive damage and requires the services of a professional contractor with a specialty in fire restoration techniques to thoroughly repair. Carpet, drywall, and trim carpentry is going to have to replaced once actually burnt rather than only receiving smoke damage. The smoke damage itself will be more extensive having had the opportunity to seep deeper into the walls and insulation. Each case is different, but it's not uncommon after a medium fire for the room where it started to need to be gutted and rebuilt.
Structural Damage from a Large Fire
It goes without saying a large fire is going to cause damage which gets into the structure of the home and can be devastating. Assuming the fire department arrives in time to prevent a total loss, your insurance company may decide differently. Your insurance adjuster will compare the age and value of the house against what it will cost to conduct the repairs and what the worth will be after the repairs to determine whether or not to rebuild the house or call it a total loss. You can expect such repairs to take at least several months during which time you and your family will have to live elsewhere.