Longitudinal fields of quantized Laguerre-Gaussian modes are derived, revealing their importance even for light that may be considered to be propagating in the paraxial regime. This is in contrast to unstructured laser light, e.g. a Gaussian beam, where the magnitude of longitudinal components only become important under strong-focusing of the source. The unique effects stem specifically from the optical angular momentum, both orbital and spin, of optical vortex light, and include spin-orbit interactions in freely-propagating circularly-polarized vortices in free-space. The contribution that longitudinal fields make to the rate of single-photon absorption is calculated, highlighting that for optical vortices they cannot be neglected in general.