No matter what time of year it is, if there are fish actively feeding on the surface and no discernible hatch is visible, the Royal coachman might be a good choice. It does a good job of mimicking several species of mayflies. It also makes an almost perfect flying ant representation (which whether you know it or not is a very common fly for fish to target). The Royal coachman I have found is particularly good in late summer-fall and is almost a mandatory fly for you to keep on hand.
Perhaps the most well known fly patterns. It is a tremendously good choice to use when there are no other flies hatching and visible on the river. The Royal coachman fly deserves a spot in your fly box.