How a Light Bulb Works
Repetitive Stress
Light bulbs burn out due to repetitive stress to the tungsten filament which produces the light. Every time a light bulb is turned on and off it heats and cools rapidly, which stresses the filament, causing it to become weaker and brittle. Also, when a light bulb is on, the filament gets so hot, that atoms from the filament gradually evaporate and then stick to the inside of the glass bulb. When a light bulb is first used, the thickness of the filament is fairly uniform and the heat is displaced evenly along it. As the filament wears, it becomes thinner in certain spots, and those spots will become disproportionately hot, further encouraging a breakdown of the filament. When the filament gets thin enough from repeated wear, it can snap, breaking the electrical current, and causing the bulb to burn out. When you shake a burnt out light bulb you can often hear a ringing sound, because fragments of the snapped filament are loose inside the bulb.
Considerations
Incandescent bulbs burn out faster than other types of bulbs, like halogen and fluorescent bulbs, because these types of bulbs take steps to reduce the stress caused by heat. Halogen bulbs compress inert gases around the filament, which allows some of the evaporated tungsten to redeposit itself back on the filament, so the degradation is slowed. With fluorescent bulbs, the primary source of light is florescence given off by a coating on the inside of the bulb. Far less heat needs to be produced in order to get a fluorescent bulb to produce the same amount of light as a normal bulb. That allows fluorescent bulbs to last much longer.