Why does the distance between the plates of a capacitor affect its capacitance?

Why does the capacitance of a capacitor increase when its plates are closer in distance to each other?

Answer

Intuitive approach: if the distance wouldn't be a factor then you would be able to place the plates at an infinite distance apart and still have the same capacitance. That doesn't make sense. You would expect a zero capacitance then.
If the capacitor is charged to a certain voltage the two plates hold charge carriers of opposite charge. Opposite charges attract each other, creating an electric field,

and the attraction is stronger the closer they are. If the distance becomes too large the charges don't feel each other's presence anymore; the electric field is too weak.