  The leading relativistic and recoil corrections to bound state $g$-factors of
particles with arbitrary spin are calculated. It is shown that these
corrections are universal for any spin and depend only on the free particle
gyromagnetic ratios. To prove this universality we develop NRQED for charged
particles with an arbitrary spin. The coefficients in the NRQED Hamiltonian for
higher spin particles are determined only by the requirements of Lorentz
invariance and local charge conservation in the respective relativistic theory.
For spin one charged particles the NRQED Hamiltonian follows from the
renormalizable QED of the charged vector bosons. We show that universality of
the leading relativistic and recoil corrections can be explained with the help
of the Bargmann-Michael-Telegdi equation.
