A quick search online shows there are dozens of different types of hiking socks, with different materials, thicknesses, and properties. In general, what should you look for when shopping for hiking socks? What are the main differences, and what would make you choose one type over another?
Don't use cotton socks for hiking.
When your feet sweat, the socks become wet, and take forever to dry out. Good socks remove the bacteria and moisture that thrive in the environment created by sweating feet and help to prevent blisters. Cotton retains moisture, thus cotton socks will not do the job properly.
Rather, buy non-itching ("merino") wool, nylon, alpaca, elastic, polyester, spandex, or polypropylene(can also be used as a layer between the sock and skin) socks.
I wear wildland firefighting boots (all leather) for work, and they can take a long time to fully break in (6-12 months!), so a good pair of socks/combination of socks is crucial. I've found that I like to wear a thin sport sock under a full boot sock, which helps to add more padding and support up to the ankle, where it counts.
A very helpful source of additional information, including more information on the different benefits of different sock types and materials: Foot Care, Socks 101 & Sock Care.