  The last decade of observational and theoretical developments in stellar and
binary evolution provides an opportunity to incorporate major improvements to
the predictions from populations synthesis models. We compute the Galactic
merger rates for NS-NS, BH-NS, and BH-BH mergers with the StarTrack code. The
most important revisions include: updated wind mass loss rates (allowing for
stellar mass black holes up to $80 \msun$), a realistic treatment of the common
envelope phase (a process that can affect merger rates by 2--3 orders of
magnitude), and a qualitatively new neutron star/black hole mass distribution
(consistent with the observed "mass gap"). Our findings include: (i) The
binding energy of the envelope plays a pivotal role in determining whether a
binary merges within a Hubble time. (ii) Our description of natal kicks from
supernovae plays an important role, especially for the formation of BH-BH
systems. (iii) The masses of BH-BH systems can be substantially increased in
the case of low metallicities or weak winds. (iv) Certain combinations of
parameters underpredict the Galactic NS-NS merger rate, and can be ruled out.
{\em (v)} Models incorporating delayed supernovae do not agree with the
observed NS/BH "mass gap", in accordance with our previous work. This is the
first in a series of three papers. The second paper will study the merger rates
of double compact objects as a function of redshift, star formation rate, and
metallicity. In the third paper we will present the detection rates for
gravitational wave observatories, using up-to-date signal waveforms and
sensitivity curves.
