Non-noncommutative geometry

You might think that non-noncommutative geometry is just geometry. But what kind, really? In other words, what is the geometry that is generalised in noncommutative geometry (NCG)? I will try to answer this by giving a (slightly fake) history of NCG as originating from a combination of C*-algebra theory, spectral geometry (hearing the shape of a drum), and some K-theory. Depending on the time, I might then sketch some cool theorems in NCG and applications in mathematics and physics.