In addition to what the other user said, people don't always have as many alarms installed as they should. There should be at least one on every floor.
But besides that, sometimes the fire just starts in an area that doesn't immediately set off the alarm due to whatever quirk of the floor plan and the passageways. If you're a heavy sleeper, and alone, in the time the alarm takes to wake you, the fire might have grown from that spot enough to block an exit.
