Bose-Einstein condensation of W bosons in the early universe is studied. It is shown that, in the broken phase of the standard electroweak theory, the condensed W bosons form a ferromagnetic state with aligned spins. In this case the primeval plasma may be spontaneously magnetized inside macroscopically large domains and form magnetic fields which may be the seeds for the observed today galactic and intergalactic fields. However, in a modified theory, e.g. in a theory with stronger quartic self interactions of gauge bosons e.g. due to a smaller value of the weak mixing angle, antiferromagnetic condensation is possible. In the latter case W bosons form scalar condensate with macroscopically large electric charge density i.e. with a large average value of the bilinear product of W-vector fields but with microscopically small average value of the field itself.