Aside from the special combos to get eggs there's also hidden ones to get goodies! To get you started here's a few for varying rings:
Brilliant Egg Ring: 1 Painted, 3 Blue, 1 Violet, 1 Yellow
Vibrant Egg Ring: 1 Colored, 2 Red, 1 Green, 1 Blue, 1 Yellow
Pristine Egg Ring: 1 Archon, 2 Yellow, 3 Red
Midnight Egg Ring: 1 Darkened, 2 Violet, 2 Red, 1 Green
Chocobo Egg Ring: Trade 3 Odd Eggs to the basket near the Egg givers.
To get this one, trade 1 of each color and 1 decorated egg (Painted, Colored, Archon, or Darkened) to the NPC. Depending on the egg you will get an egg hat from last year's Hatching-Tide event. But you already have the hat (in your inventory) you'll get an Odd Egg instead.
There's also a Motley Egg found from 3 NPC Spriggans in the outlying areas. First is standing near the road leaving Camp Blackbrush in Thanalan going west towards Camp Horizon. Second is along the road in a stream in the center of the pathways going between both Gridanian entrances (29, 30) in the Black Shroud. Third is a tad trickier. Going south from the gates out of Limsa Lominsa you'll see a bridge (On the edge of 25, 34) where the third is. Speaking to one rewards you with the Motley Egg, but voids the other two from giving an egg as well. The treat about this egg is it can be used to replace one of the decorated eggs in any combo! Can't get a painted archon egg? Substitute this egg in exchange when presenting the combo.
This site has info on where to find the spriggans too for collecting eggs: http://ffxiv.gamerescape.com/wiki/Ha...ide_%282012%29
And now for a secret little tidbit~ Pay attention to the fireworks that appear at night, these too are a secret combo! While they won't net you a ring, hat, or anything special they will net a much better reward than the normal ones! Just trade in any decorated egg and the 5 eggs that appear in the firework sequence. Doing so netted me 3 hi-potions of intelligence. For easiest viewing just go to Limsa Lominsa and view the firework display from the cliffside near the Egg Event NPCs. Happy hunting!
EDIT: If you can't find the best place to view the fireworks just find the "Skyward Spriggan" and face the direction it looks. In Ul'dah this fellow can be found in the area just above the center steps facing the entrance into the city. (Near the Adventurer's Guild and the row of vendors heading towards the Gold Court.) I haven't found the one in Gridania but I'm tired so hopefully somebody else can point this one out.