How do I link Particle data between objects? Normally if I have a material and want to put that material on say, 50 different objects, then I would select one object with that material, and then select the rest of the objects, hit Ctrl + L, and the material data would be copied to all the objects.

I have the exact situation I described above, except that I want to copy an object constraint from one object to all the other objects. Unfortunately the Ctrl + L menu doesn't have a "Particle" button.

How do I copy this Part to all the other objects?
select all the objects you want the particle system to be linked to
select the object with particle system as last (so it is the active object)
from particle system list select the system to be linked (the active one or all the particle systems)