Conventional and spin related thermoelectric effects in zigzag boron nitride nanoribbons are studied theoretically within the Density Functional Theory (DFT) approach. Nanoribbons with edges passivated with hydrogen, as well as those with bare edges are analyzed. It is shown that one spin channel in the nanoribbons of 0HB-0HN and 2HB-1HN types becomes nonconductive slightly above the Fermi level, and therefore such nanoribbons reveal remarkable spin related thermoelectric phenomena and are promising materials for thermoelectric nanodevices. Thermoelectricity in BN nanoribbons of other types is less efficient and therefore these materials are less interesting for applications.