Minecraft wiki entry for Smelting, associated text: When the furnace runs out of smeltable items: That is, the input slot becomes empty.
The furnace runs out of fuel: The fuel input slot is empty and the current fuel item is fully consumed (that is, the fuel gauge becomes empty).
The output slot becomes full: Either the slot has a full stack of the output, or the output contains the wrong output item for the current input item. (For example, if the output contains iron ingots but the input contains raw gold.) In this case, smelting (but not fuel consumption) is paused until the output slot becomes available (usually because items were removed by either a player or a hopper). If a fuel item burns out in this condition, a new one is not used until the output slot is again available.
The furnace is broken: The contents of all the slots, any accumulated experience, and the furnace itself are dropped. The currently-burning fuel item is lost, since it is removed from the fuel slot before burning begins. The furnace block itself may not be dropped if it was destroyed by an explosion.