  We estimate the contribution of Galactic pulsars, both ordinary and
millisecond pulsars (MSPs), to the high-energy (>100 MeV) gamma-ray background.
We pay particular attention to the high-latitude part of the background that
could be confused with an extragalactic component in existing analyses that
subtract a Galactic cosmic-ray model. Our pulsar population models are
calibrated to the results of large-scale radio surveys and we employ a simple
empirical gamma-ray luminosity calibration to the spin-down rate that provides
a good fit to existing data. We find that while ordinary pulsars are expected
to contribute only a fraction ~10^-3 of the high-latitude gamma-ray intensity
(I_X~1x10^-5 ph s^-1 cm^-2 sr^-1), MSPs could provide a much larger
contribution and even potentially overproduce it, depending on the model
parameters. We explore these dependences using a range of MSP models as a guide
to how gamma-ray measurements can usefully constrain the MSP population.
Existing gamma-ray background measurements and source counts already rule out
several models. Finally, we show how fluctuations in the gamma-ray sky can be
used to distinguish between different sources of the background.
