When are studded tires necessary?
I find them useful on the street during the winter. Here in Minneapolis it gets pretty cold and the streets can get pretty icy. Their studded-ness plus their aggressive tread pattern give me good traction in snow and on ice.

However, studded tires are really slow. The majority of the time, even in winter, there isn't much ice and I am completely fine riding on slicks. For days when its snowing and icy, I have a spare front wheel with a studded tire mounted on it. I'll swap that in for those days, leaving the slick on the back. Traction on the back is less than optimal, but it is a good speed/stability tradeoff. I can handle my backwheel slipping around, but if the front wheel slips I am going to end up on my face. 

Also I did this when I commuted daily, so I didn't skip very snowy days. In fact very snowy days made me want to ride more.