1. Ferromagnetism eg permanent magnets. This is where all the magnetic moments align in the same direction (this is how you get north pole and south pole). The strongest magnet known is a neodymium-iron-boron compound (Nd2Fe14B), which is used in earphones and high-performance speakers.
2. Anti-ferromagnetism - magnetic moments align in opposite directions and cancel leaving no net moments.
3. Ferrimagnetism - moments align in opposite directions leaving net residual moment. There is a family of compound called rare earth garnets (Ln3Fe5O12), a complex oxide. Its ferrimagnetic properties have unsual temperature dependence.
Let's say the lanthanide has bigger moments and is pointing up; and the iron has smaller moments pointing in opposite direction. This results in a net magnetic moment pointing up. However, as you heat the compound, the lanthanide magnetic moment is destroyed leaving only the iron's magnetic moment which is pointing in a different direction. So the overall effect is a change of direction of magnetic moment on heating the compound.
Personally, I find this quite fascinating.