Informal introduction to Grothendieck topologies

I trot out all the opinions and jokes I can remember about G-topologies. Finding appropriate formal definitions or properties is not necessarily my forte (for which see http://en.wikipedia.org/wiki/Grothendieck_topology.) Grothendieck topologies or sites or topoi are just categories with the categorical properties of categories of sheaves, so that they are just a little technical vehicle for cohomogy. What you actually do with them depends on the actual context, and usually involves a lot of detailed hard work. Classical topology, Zariski topology, etale topology, fppf and fpqc flat topologies, crystalline site, rigid analytic G-topology.