  In this paper, the first of a series, we study the stellar dynamical and
evolutionary processes leading to the formation of compact binaries containing
white dwarfs in dense globular clusters. We examine the processes leading to
the creation of X-ray binaries such as cataclysmic variables and AM CVn
systems. Using numerical simulations, we identify the dominant formation
channels and we predict the expected numbers and characteristics of detectable
systems, emphasizing how the cluster sources differ from the field population.
We explore the dependence of formation rates on cluster properties and we
explain in particular why the distribution of cataclysmic variables has only a
weak dependence on cluster density. We also discuss the frequency of dwarf nova
outbursts in globular clusters and their connection with moderately strong
white dwarf magnetic fields. We examine the rate of Type Ia supernovae via both
single and double degenerate channels in clusters and we argue that those rates
may contribute to the total SN Ia rate in elliptical galaxies. Considering
coalescing white dwarf binaries we discuss possible constraints on the common
envelope evolution of their progenitors and we derive theoretical expectations
for gravitational wave detection by LISA.
