  We introduce a new, very deep neutral hydrogen (HI) survey being performed
with the Westerbork Synthesis Radio Telescope (WSRT). The Westerbork Hydrogen
Accretion in LOcal GAlaxieS (HALOGAS) Survey is producing an archive of some of
the most sensitive HI observations available, on the angular scales which are
most useful for studying faint, diffuse gas in and around nearby galaxies. The
survey data are being used to perform careful modeling of the galaxies,
characterizing their gas content, morphology, and kinematics, with the primary
goal of revealing the global characteristics of cold gas accretion onto spiral
galaxies in the local Universe. In this paper, we describe the survey sample
selection, the data acquisition, reduction, and analysis, and present the data
products obtained during our pilot program, which consists of UGC 2082, NGC
672, NGC 925, and NGC 4565. The observations reveal a first glimpse of the
picture that the full HALOGAS project aims to illuminate: the properties of
accreting HI in different types of spirals, and across a range of galactic
environments. None of the pilot survey galaxies hosts an HI halo of the scale
of NGC 891, but all show varying indications of halo gas features. We compare
the properties of detected features in the pilot survey galaxies with their
global characteristics, and discuss similarities and differences with NGC 891
and NGC 2403.
