Blue is not rare to see in nature — sky and water both commonly appear blue — but a genuine blue biological pigment is comparatively rare. Most blue-appearing animals, including many blue birds and butterflies, produce the colour structurally: microscopic structures in feathers, scales or skin scatter light so that blue wavelengths dominate, without any blue pigment being present at all.

The sky looks blue because air molecules scatter shorter (blue) wavelengths of sunlight far more than longer (red) wavelengths — a phenomenon called Rayleigh scattering. Near the horizon, light passes through more atmosphere and loses more blue, which is why the sky looks paler there.
Sky colour varies continuously with time of day, humidity, pollution and altitude; this is one clear-weather example, not a universal reference blue."Blue Sky" by Shubhamk483, CC BY 4.0, via Wikimedia Commons
Blue Jay feathers contain no blue pigment whatsoever. Microscopic air pockets in the feather's structure scatter short wavelengths of light back as blue — the same reason a clear sky looks blue rather than colourless.
Like the Blue Morpho and the peacock, a Blue Jay's blue is structural, not pigment: a crushed or backlit feather shows no blue at all."Blue Jay" by IzzyMPhotography, CC BY-SA 4.0, via Wikimedia CommonsMicroscopic physical structures — ridges, layers or particles smaller than the wavelength of light — interfere with light waves so that only certain wavelengths are reflected back. No pigment is involved at all.
Common misconception: A structurally-coloured feather or scale ground into powder loses its colour completely, because grinding destroys the microscopic structure that produced it.
Particles or molecules much smaller than the wavelength of light scatter shorter (blue) wavelengths far more than longer (red) ones — the reason a clear daytime sky looks blue and a low sun looks orange or red.
Most blue colouration in birds — such as blue jays and many other species — is produced structurally, by microscopic keratin structures in the feather barbs that scatter blue wavelengths of light, rather than by a blue pigment.
Birds · confidence: high
Many blue butterflies, including morpho butterflies, produce their vivid blue through microscopic scale structures that reflect blue light through interference effects, not through a blue pigment in the wing.
Insects · confidence: high
A small number of organisms, including some flowers and marine species, do produce genuine blue pigments, but this remains comparatively uncommon relative to the number of organisms that appear blue overall.
Plants · confidence: medium
Sky and open water frequently appear blue to human observers, but this is a perceived environmental colour caused by light scattering and absorption, entirely separate from the question of whether blue pigments are common in living organisms.
Sky and atmosphere · confidence: high
Common structural rare chemical
Birds · blue-plumaged bird species · qualitative review of documented feather-structure studies
Refers specifically to the pigment-vs-structure mechanism, not to how often blue birds are observed.
Frequency and rarity claims above are scoped to a specific domain, geography or taxonomic group — none are presented as a single universal ranking. See methodology.