  We report observations of Faraday rotation measures (RMs) for a sample of 191
extragalactic radio jets observed within the MOJAVE program. Multifrequency
VLBA observations were carried out over twelve epochs in 2006 at four
frequencies between 8 and 15 GHz. We detect parsec-scale Faraday RMs in 149
sources and find the quasars to have larger RMs on average than BL Lac objects.
The median core RMs are significantly higher than in the jet components. This
is especially true for quasars where we detect a significant negative
correlation between the magnitude of the RM and the de-projected distance from
the core. We perform detailed simulations of the observational errors of total
intensity, polarization and Faraday rotation, and concentrate on the errors of
transverse Faraday RM gradients in unresolved jets. Our simulations show that
the finite image restoring beam size has a significant effect on the observed
RM gradients, and spurious gradients can occur due to noise in the data if the
jet is less than two beams wide in polarization. We detect significant
transverse RM gradients in four sources (0923+392, 1226+023, 2230+114 and
2251+158). In 1226+023 the RM is for the first time seen to change sign from
positive to negative over the transverse cuts, which supports the presence of a
helical magnetic field in the jet. In this source we also detect variations in
the jet RM over a time scale of three months, which are difficult to explain
with external Faraday screens and suggest internal Faraday rotation. By
comparing fractional polarization changes in jet components between the four
frequency bands to depolarization models we find that an external purely random
Faraday screen viewed through only a few lines of sight can explain most of our
polarization observations but in some sources, such as 1226+023 and 2251+158,
internal Faraday rotation is needed.
