The discovery of a Standard Model-like Higgs boson and the hitherto absence of evidence for other new states may indicate that if WIMPs comprise cosmological dark matter, they are heavy compared to electroweak scale particles, M >> m_{W^\pm}, m_{Z^0}. In this limit, the absolute cross section for a WIMP of given electroweak quantum numbers to scatter from a nucleon becomes computable in terms of Standard Model parameters. We develop effective field theory techniques to analyze the heavy WIMP limit of WIMP-nucleon scattering, and present the first complete calculation of the leading spin-independent cross section in Standard Model extensions consisting of one or two electroweak SU(2)_W x U(1)_Y multiplets. A new extension of the effective theory to describe heavy WIMP annihilations is discussed.