Chemisorption of sulfides and alkanethiols on Ag(111) is studied by scanning tunneling microscopy (STM). Adsorption of sulfide from aqueous solutions of Na2S and H2S or from gas phase with H2S, respectively, leads to a highly ordered hexagonal adsorbate lattice (alpha(1) = 440 +/- 10 pm) with a (root 7 x root 7)-R10.9 degrees coincidence cell. A slightly denser packed hexagonal lattice (alpha(2) = 435 +/- 10 pm) with a (3 x 3) coincidence cell is found only on a small fraction of the surface. An inherent Moire pattern which can be observed in both cases allows distinguishing the two very similar adsorbate lattices and evaluating adlayer models. Self-assembling of alkanethiols (H-(CH2)(n)SH; n = 1, 2, 4, 6, 8, 9, 10, 11) and dimethyl disulfide from organic solution results in a hexagonal adsorbate lattice (alpha(3) = 440 +/- 15 pm). A (root 7 x root 7)R10.9 degrees coincidence cell, as observed for the sulfide adlayer can be proven only for adsorbed methanethiolate. For an increasing n alkyl chain length a monotonous increase in the tunneling resistance is necessary to maintain molecular resolution. This can be regarded as a direct proof for the presence of the alkyl chains in the tunneling gap during imaging. In the case of hexanethiol the formation of the self-assembled monolayer has also been studied in situ.