Everything rotates at some rate. The rotation-powered pulsars mentioned in ProfRob's answer need to spin fast to generate their radiation. Accretion-powered pulsars do not, so they may be observed at slower rotation rates. The slowest one known is AX J1910.7+0917, at a period of about 36,200 seconds. This is extremely slow for such a dense object, with angular momentum/mass of ~0.001% of Earth.
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The pulsed emission from an accretion-powered pulsar is thermal. The pulsar accretes matter from a binary companion. The pulsar's magnetic field channels the accreted matter, which impacts and heats the pulsar at hot spots. The changing visibility of the hot spots as the pulsar rotates is observed as pulsating x-rays. If the magnetic field is strong enough, it can also channel the x-rays into beams, enhancing the effect.
Over the short term, accretion-powered pulsars are very regular. Over the long term, the accretion torques the pulsar, changing its period. As an extreme example, GX1+4's period decreased at ~2% per year through the 1970's.