We report first-principles calculations that clarify stability and electronic structures of silicene on Ag(111) surfaces. We find that several stable structures exist for silicene/Ag(111), exhibiting a variety of images of scanning tunneling microscopy. We also find that Dirac electrons are {em absent} near Fermi energy in all the stable structures due to buckling of the Si monolayer and mixing between Si and Ag orbitals. We instead propose that either BN substrate or hydrogen processing of Si surface is a good candidate to preserve Dirac electrons in silicene.