That's a good question.
To start with, I'd say it's more than simply "said" that energy can't be destroyed. That statement is part of the First Law of Thermodynamics. The full statement of that law gives you the answer, I think: Energy can be transformed, but it cannot be created or destroyed.
The light energy from a lightbulb is probably mostly transformed into heat energy. Think about the light bulb as a little sun, sending out radiant energy (visible light and other EM radiation) that strikes objects and warms them. Of course, the amount of heat (thermal energy) absorbed by our skin from the light of a single lightbulb would be pretty hard to notice. (A hot incandescent lightbulb itself, of course, would be a different matter altogether. Touching a hot lightbulb is not a good idea.)
Another way to answer your question would be to say that the concentrated energy (from the power source to the light bulb) is released or broadcasted into a larger area and disperses according the law of entropy. The energy doesn't vanish; it simple gets spread out and becomes a whole lot less noticeable. Think of a cupful of boiling water poured into a swimming pool full of water at room temperature: the entire pool of water will be warmed just ever so slightly by that cup of boiling water.
Light energy continues to travel with light as the light travels along its path unrestricted, just as the energy in water waves travels along with the waves. Light is capable of travelling like this for ever covering infinite distance, and in this way preserve the light energy. Of course, as stated in answer above the light spreads out as it travels faster and with that the energy in light also gets spread out over larger space as light travels forward.
When the light strikes a surface or material that does not allows the light to travel forward, and instead absorbs it the light energy gets transformed in other forms. Most common of these form is heat. But it can get converted in other forms also. For example, light striking a photo-electric cell converts it in electric energy. Also light striking leaves of trees gets converted in chemical energy that causes carbon dioxide in atmosphere to combine with chemicals in the plant to form food for the plant, releasing oxygen gas.