  We investigate the number and type of pulsars that will be discovered with
the low-frequency radio telescope LOFAR. We consider different search
strategies for the Galaxy, for globular clusters and for other galaxies. We
show that a 25-day all-sky Galactic survey can find approximately 900 new
pulsars, probing the local pulsar population to a deep luminosity limit. For
targets of smaller angular size such as globular clusters and galaxies many
LOFAR stations can be combined coherently, to make use of the full sensitivity.
Searches of nearby northern-sky globular clusters can find new low luminosity
millisecond pulsars. Giant pulses from Crab-like extragalactic pulsars can be
detected out to over a Mpc.
