I believe the rarest are the 4 dino species. I think if you add all 4 of them together, you get about as many as the next rarest thing which I think is the chicken. As far as actual dragons, gold, silver, and paper are rare. Two headeds are also supposed to be rare, but part of the code that decides which egg to distribute also looks at how many already exists, and tries to keep it in balance with how rare each one is supposed to be. So female 2 headeds, which didn't exist at all for a long time, are still trying to "catch up" for all that time when there were none of them so they are relatively common right now but the male 2 headeds are still rare.
Note this is not official information by any means, just based on my own observations. The bit about it being coded to try to keep the distribution in balance did come from TJ.