  A sample of large northern Spitzer Infrared Nearby Galaxies Survey (SINGS)
galaxies has recently been observed with the Westerbork Synthesis Radio
Telescope (WSRT). We present observations of the linearly polarized radio
continuum emission in this WSRT-SINGS galaxy sample. Of the 28 galaxies treated
in this paper, 21 are detected in polarized radio continuum at 18- and 22-cm
wavelengths. We utilize the rotation measure synthesis (RM-Synthesis) method,
as implemented by Brentjens & de Bruyn, to coherently detect polarized emission
from a large fractional bandwidth, while simultaneously assessing the degree of
Faraday rotation experienced by the radiation along each line-of-sight. This
represents the first time that the polarized emission and its Faraday rotation
have been systematically probed down to ~10 microJy/beam RMS for a large sample
of galaxies. Non-zero Faraday rotation is found to be ubiquitous in all of the
target fields, from both the Galactic foreground and the target galaxies
themselves. In this paper, we present an overview of the polarized emission
detected in each of the WSRT-SINGS galaxies. The most prominent trend is a
systematic modulation of the polarized intensity with galactic azimuth, such
that a global minimum in the polarized intensity is seen toward the
kinematically receding major axis. The implied large-scale magnetic field
geometry is discussed in a companion paper. A second novel result is the
detection of multiple nuclear Faraday depth components that are offset to both
positive and negative RM by 100-200 rad/m^2 in all targets that host polarized
(circum-)nuclear emission.
