One of the first parts of the lawn to green up in the spring are the circular fungal infections called fairy rings. While fairy rings are not particularly attractive, they are not terribly damaging to lawns, and most people just learn to live with them. One reason is that there are not really any good ways to get rid of them, except by digging up the entire infested area to a depth of two feet and at least one foot beyond the outer edges of the ring. If you choose this method, dispose of the infected soil, taking care not to spill any on healthy lawn. But because fairy rings do not really destroy turf, most people just ignore them.
There are some techniques for minimizing the rings, however. Remove and discard the mushrooms that usually develop around the edge of the rings. Because the fungus does well in dry, underfertilized lawn, spike the area with a spading fork every few days, and water it well. Encourage beneficial soil microbes by the application of organic fertilizers and by topdressing with humus builders such as finished compost, or commercial products like Lawn Restore or Vitabuild. Supplemental nitrogen can help compensate for temporary nitrogen tie-up by beneficial microbes.
A remedy I have heard about is to wait for a full moon, set a comfortable lawn chair out, and with a 6-pack of your favorite beverage try and catch the fairy that is responsible for the rings; the theory goes, even if you don't catch the culprit, by the time your beverage is gone, you won't care about the rings anymore. This remedy is said to be ineffective, but enjoyable.
References:
Shurtleff, M., W. Thomas, and R. Randell. 1987. Controlling Turfgrass Pests. Prentice-Hall, Inc. Englewood Cliffs, NJ 07362. 449 pp.