What is the shielding in nuclear reactors mainly against? I have a little knowledge about ionizing radiation and I have been confused over why nuclear reactors need these massive shields.
So, if I am not mistaken, Alpha and Beta radiation are not that dangerous since they can be shielded with relatively light materials, the main problem is because Gamma and Neutron radiation.
So now, which one requires that heavy shielding ?
Also, if the reactor released either Gamma rays only or Neutrons only, which one of them would need less massive material to be reduced to a non-harmful level ?
Any numbers on the density of radiation this shield has to stop will greatly help here too.
 A: Yes, heavy shielding is needed primarily for gamma radiation. Neutron radiation (with energies seen in fission reactors) is easily stopped with boron-10 (isotopically enriched boric acid in water).
While alpha and beta radiation is easier to shield, it is even more dangerous if alpha and beta active particles (dust) is consumed by human, because they will irradiate you for many years, and all their energy would be consumed by your body. So it's obviously important to physically contain high-pressure radioactive material inside reactor. 
Regarding shielding of gamma radiation: it is usually done by materials with high atomic mass (lead, depleted uranium e.t.c). It can be done with lighter materials with comparable mass (i.e. water shield must be ~10 times thicker, than lead one). Depending on gamma ray energy, you might need about 1-10cm of lead to consume 50% of gamma radiation. Some more details are here : http://en.wikipedia.org/wiki/Gamma_ray#Shielding
A: I'm not an expert and I know we have some people on the site who are much closer to being experts, but there are several points that I can offer to tide you over.


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*A large fraction of the precautions taken in reactor design are for protection in the event that things have gone wrong, rather than necessary in the course of typical running. 

*Much thought also goes into containing activated material: the primary radiation can transmute atoms near the core. Sometimes the resulting atoms are radioactive themselves. In the absence of careful testing and strictly enforced procedures, these materials can then be carried outside of the containment area by the movement of air, people, machines or water. Especially water, because the primary water has to be pumped through a heat exchanger to transfer the energy to the secondary loop which means lot of joints and moving parts.

*The high temperatures and pressures in the water system can be brutal on equipment (this is the case in all steam power systems, but it is harder to clean up after if the water is tritiated).

*If the fuel gets out of the fuel rods (even one) themselves you have a vast amount of material to clean up. 

*The design of the containment vessel is typically expected to provide protection against impact from large vehicles and attacks involving moderate amounts of explosives.
