The structural properties of individual darkmatter haloes, including shape, spin, concentration, and substructure, are linked to the halo's growth history, but the exact connection between the two is unclear. One open question, in particular, is the effect of major mergers on halo structure. We have performed a large set of simulations of binary equal-mass mergers between isolated haloes with various density profiles, to map out the relationship between the initial conditions and merger parameters and the structure of the final remnant. In this paper we describe our initial set-up and analysis methods, and report on the results for the size, shape, and spin of the merger remnant. The outcomes of mergers are most easily understood in terms of a scaled dimensionless energy parameter. and an angular momentum (or spin) parameter lambda. We find that the axial ratio c/a scales roughly linearly with energy kappa while the axial ratio c/b scales linearly with spin lambda. Qualitatively, mergers on radial orbits produce prolate remnants, while mergers on tangential orbits produce oblate remnants. The spin of the remnant can be predicted from angular momentum conservation, while the overall size changes as similar to kappa(-5), as expected from self-similar scaling at constant mean density. We discuss potential cosmological applications for these simple patterns.