In current-free stellarators, the parallel current density is normally too weak to drive global external kink modes. However, at finite values of beta, the bootstrap current (BC) can provide sufficient free energy to trigger this class of mode in some stellarator systems. The effect of the BC in the collisionless 1/nu regime has been investigated in several different types of stellarator reactor systems all with a volume V similar to 1000 m(3). In quasiaxisymmetric and quasihelically symmetric stellarators, the BC is large at, finite beta and this can cause low order resonances to move into and emerge out of the plasma which in turn can destabilize global internal and external kink modes. In a six-field period system with poloidally closed contours of the magnetic field strength B, the BC is small and decreases the rotational transform only slightly. As a result, only intermediate to high n modes can become weakly destabilized. Furthermore, it is demonstrated in this system that the contours of the second adiabatic invariant J(parallel to) close poloidally for all trapped particles at finite beta* similar to 6%. This condition leads to the loss of a very small fraction of the collisionless alpha-particle orbits. In Sphellamak configurations with peaked toroidal currents required to generate nearly isodynamic maximum-B confining field structures, the BC accounts only for a small fraction of the total current. The loss of a-particles born within the inner quarter of the plasma volume is negligible while about 1/3 of those born at half volume escape the device within a slowing down time.