I don't have any rare Pokémon. Lol. Hoping that will change though when I'm finally able to spend pokepoints on Pokeballs and stuff.
I pride myself in having some rare mons. As it stands... my Snorlax, Chansey, Lairon, Lapras, Empoleon, and Dunsparce.
I would think Shiny Mew since it's a shiny legendary and there is only a certain time frame you can get one with the odds in your favor... however, I still have a shiny lv1 Jynx I got ages ago. Since Jynx is no longer able to be caught in the catcher and Smoochum is only available as a hatched variant from an Odd Egg... it makes shiny Jynx pretty rare from a statistical standpoint.
I'm honestly not sure if Shiny Mew counts as rare, because while it was only available for a certain time to catch fresh, there were a fair amount of them caught, which drove down the value. So I couldn't say for sure, or make an objective judgment, on how rare it is. Unless you're Mandriel, in which case your shiny Mew is the rarest of all.
I have some shiny legend eggs and two shiny hoopa and three shiny darkrai. But apparently there is an event, so I suppose they arent that rare.