There are only a few truly iconic dry fly patterns. Flies that seem so familiar and necessary that you don't ever question their origins or whether you select a few for your next trip. They are in your box and they will always be in your box. They just ARE!
If you were making a list, the Adams and the variations of the Quill Gordon from the Catskill-style era would be sure bets. As would be the Light (and Dark) Cahill (circa 1884). These are the iconic mayfly patterns. For the midge its the Griffith's Gnat. You would have to throw a parachute Adams in there too. It works as both a mayfly and as a midge. There is not a trout fisherman alive that does not have some of these flies in their go-to box.
But for caddis, there is really only one classic pattern... the Elk Hair Caddis. It is THE caddis pattern. The inventor, Al Troth, passed away August 3. He was 82. Thanks Al and have a good journey. I hope there is a trout stream there.