If you live in a humid are, you will often find that you stone patio will get mildewy. Sometimes this is caused by improper draining, or if there is inadequate airing of the stones, as in the case of a patio that is surrounded by vegetation. Fortunately there are ways to combat this scourge.
There are a variety of solutions you can use to clean the stones. If you are environmentally or budget conscious, you can use simple white vinegar. Experiment with a small area before applying to the entire area. Not all stone behaves the same.
Another solution calls for oxygen bleach, which is different from chlorine bleach. The difference is that oxygen bleach releases oxygen when it is combined with water. It has the added benefit of being less toxic than chlorine. Unfortunately oxygen bleach is not as effective as its chlorine brother, but you have to take the bad with the good. Chlorine bleach will kill vegetation in your garden.
Finally, there is a number of commercial products that are made specifically for cleaning patio stones. These solutions do not use any bleach and they will not fade the colors of the stones.
If all else fails, you can always rent a pressure washer.