In this paper, we investigate the Sherman-Morrison-Woodbury formula for the {1}-inverses and the {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A + YGZ *) ⊙ = A ⊙ − A ⊙ Y(G ⊙ + Z * A ⊙ Y) ⊙ Z * A ⊙ holds, where A ⊙ stands for any kind of standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose inverse, Drazin inverse, group inverse, core inverse and dual core inverse of A.