I have ten fairy rings in my courtyard. Do I live in the Magic Kingdom? No, I just happen to have an abundant fruiting of a tiny mushroom called Arrhenia retiruga growing on the moss that covers the bricks. I have seen it in the past two years, but never as numerous as it is now, at the end of October 2011. Although it sounds as if you are clearing your throat when you say it, this genus was actually named in honour of a botanist called J.P. Arrhenius.
The fruit bodies are tiny - mostly only a few millimetres across - and tend to be one-sided, thin and rather petal-like, without a stipe. The hymenium is almost smooth, with shallow veins, but nothing resembling gills. The main reason it is growing at my house is the moss that covers much of our small courtyard - this fungus is almost always associated with mosses, and doesn't seem to be a particularly congenial companion, since the moss looks a bit faded wherever the Arrhenia is growing.