  The structural properties of individual dark matter 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 $\kappa$ and an angular momentum (or spin) parameter $\lambda$. We
find that the axis ratio $c/a$ scales roughly linearly with energy $\kappa$
while the axis 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 $\sim
\kappa^{-5}$, as expected from self-similar scaling at constant mean density.
We discuss potential cosmological applications for these simple patterns.
