  It has been proposed recently that the scale of strong gravity can be very
close to the weak scale. Dimensions of sizes anywhere from $\sim $mm to $\sim
$TeV$^{-1}$ can be populated by bulk gravitons, vector bosons and fermions. In
this paper the one-loop correction of these bulk particles to the muon magnetic
moment (MMM) are investigated. In all the scenarios considered here it is found
that the natural value for the MMM is $O(10^{-8}-10^{-9})$. One main result is
that the contribution of each Kaluza$-$Klein graviton to the MMM is remarkably
finite. The bulk graviton loop implies a limit of $\sim 400$ GeV on the scale
of strong gravity. This could be pushed up to $\sim 1-2$ TeV, even in the case
of six extra dimensions, if the BNL E821 experiment reaches an expected
sensitivity of $\sim 10^{-9}$. Limits on a bulk $B-L$ gauge boson are
interesting, but still allow for forces $10^6-10^7$ times stronger than gravity
at mm$^{-1}$ distances. The correction of a bulk right-handed neutrino to the
MMM in one recent proposal for generating small Dirac neutrino masses is
considered in the context of a two Higgs doublet model, and is found to be
close to $10^{-9}$. The contributions of all these bulk particles to the MMM
are (roughly) independent of both the total number of extra dimensions and the
dimension of the subspace occupied by the bulk states. Finally, limits on the
size of ``small'' compact dimensions gotten from the MMM and atomic parity
violation are determined and compared.
