The electronic spectra of long carbon nanotubes (CNTs) can, to a very good approximation, be obtained using the dispersion relation of graphene with both angular and axial periodic boundary conditions. In short CNTs one must account for the presence of open ends, which may give rise to states localized at the edges. When a magnetic field is applied parallel to the tube axis, it modifies both momentum quantization conditions, causing hitherto extended states to localize near the ends. We study analytically and numerically the appearance and evolution of this peculiar localization phenomenon in CNTs of any nonarmchair chirality, including the electron spin. Conductance calculations show different evolution of spin up and down states in increasing magnetic field.