We study the predictions of several extensions of the standard model (SM) for the ratio R = N(pp-bar..-->..W..-->..e..nu..)/N(pp-bar..-->..Z..-->..e/sup +/e/sup -/). The starting point of our investigation is the observation that the SM prediction for R seems to be somewhat above the data, especially if the top quark is heavy. We first show that this situation is not changed qualitatively by the incorporation of full quark-mass-dependent QCD corrections for GAMMA/sub W/ and GAMMA/sub Z/. However, if either gauginos or exotic E(6) leptons with suitably chosen masses and mixings are present, the prediction for R can be reduced by 0.5--0.7 units. A similar reduction is possible if the Z boson mixes with the Z' boson present in certain SO(10) and E(6) models. For large top masses the reduction of R can be even larger if the b quark has a sizable SU(2)-singlet component, which is possible in superstring-inspired E(6) models. However, sleptons or squarks cannot reduce the prediction for R, and in models with two Higgs doublets R is expected to be close to its SM value. We then show that existing data strongly disfavor a sequential down-type quark below 26 GeV, and derive limits on the V/sub t//sub b/ element ofmore » the extended Kobayashi-Maskawa mixing matrix of four-generation models. We also show that the data on R together with existing bounds on the rho parameter severely constrain models of four-generation quark mass matrices.« less