Schemes were invented in the early 1960s, and Grothendieck wasn't the only one involved in their development (though he is usually credited with their invention) - I think it was Serre who first defined Spec(A)

and its structure sheaf (hence affine schemes); Cartan came up with the idea of ringed spaces (at least this is what I gather from reading the excellent introduction to EGA I, Grundlehren edition). And of course, the fundamental analogy is: schemes / affine schemes = manifolds / euclidean spaces.