We perform first-principles calculations to investigate the behavior of orbital moments (OM's) of $3d$ impurities in Cu, Ag, and Au. Previous calculations for Fe impurities in Ag and Au indicate that in Ag, where the d band is located at lower energies, the Fe impurity has a significant OM, while in Au, where the shallower d band hybridizes strongly with the Fe d levels, the OM is extremely small, practically quenched. One of our objectives here is to determine whether the OM's of other $3d$ impurities in Au are equally suppressed, indicating the importance of hybridization with the shallow d-band of the host Au, or if they can be significantly large. We find that, in spite of the importance of hybridization, the behavior of the OM's of $3d$ impurities in Cu, Ag, and Au is not primarily governed by the position of the d band of the host. For all the hosts considered here, the OM's are negative for early $3d$ impurities and positive for Fe and Co. This behavior, reminiscent of Hund's rule, can be understood in terms of the width and the occupation of the virtual bound states of the up and down bands at the impurity site.