I was looking over some picture of guys who have overly thick necks--how does this happen? I imagine shrugs probably work some of the lower areas, but is there any muscle training specialized for that area?
Neck rolls very slow and deliberate are a good start. You do them isometric style contracting the muscles and going through the motion. Later when you have some strength do bridging supporting your body through your head. Scrawny neck muscles are a sign of protein deficiency.
Thick neck comes with a lot of medical conditions.
You are prone to breathing prolems and sleep apnea.
You are prone to early onset of cervical facet DJD.
Working out with weights on your neck and shruggs is just asking for trouble. The brachial plexus nerve bundle is sandiwiched between the anterior and middle scalenes of the neck muscles. Tighented neck scalene muscles can impinge on your brachial plexus nerve bundle supplying your entire upper extremity, causing Thoracic Outlet Syndrome.