During the last five years, the existence of a d-wave pairing state in several cuprate high-temperature superconductors has been firmly established by Josephson tunneling, London penetration depth, photo emission, Raman scattering, and other experimental probes. Yet, at least in some cuprate materials, there is also mounting evidence for a fully gapped conventional s-wave pairing state. In this seminar talk I will revisit the question of competing pairing states by studying the screening of the effective electron-electron interaction potential within the framework of Hubbard and extended Hubbard strongly correlated electron models. I will show that, in the presence of a sufficiently strong on-site Coulomb repulsion U, the screened interaction potential V_S develops a strong "overscreening" effect as the electron band filling is changed by doping away from the insulating half-filled band limit. At lower doping, <~15%, V_S thus develops a near neighbor attraction which can support a d-wave pairing state. At larger doping, >~15%, even the on-site U repulsion is supressed by the overscreening effect and the screened on-site potential becomes attractive, thereby supporting an s-wave pairing state. An exact proof for the existence of on-site overscreening will be presented. Implications of the overscreening effect for possible novel s weak-coupling approaches to the strongly correlated electron problem will be discussed.