Turkey Vulture (Cathartes aura)
If you see a vulture (or a buzzard, if you prefer) in New Mexico, it's safe to assume that it's a turkey vulture. The adults' bare red heads make it easy to clinch the ID. When gliding, turkey vultures tend to hold their wings in a shallow V (dihedral) and to teeter a bit. The undersides of the flight feathers look lighter than the rest of the bird.
Juvenile turkey vultures have black heads, which might tempt you to misidentify them as black vultures (Coragyps atratus). However, that species almost never visits the state.