Legendary Birds: Super rare. They're pretty much just very powerful Pokemon. Also they make nests so it assumed they also breed, they're just very exclusive about it.
Mew: Super rare. Being its (supposedly) the ancestor of all Pokemon, that mean probably in the beginning there were only Mew. However Arceus made them with unstable DNA so that they would rapidly evolve into different kinds of Pokemon based on their environment. So probably 99.9~% of all Mews have turned into different species of Pokemon. However, for one reason or another, some Mews have been able to keep their form and able to keep a stable breeding population (and they also probably have a long life span).
Mewtwo: Super rare. HEAR ME OUT! I have reasons. Though many Mewtwo are probably man made (there must have been a team of scientists working to make Mewtwo along with Mr. Fuji, and I wouldn't be surprised if some moved onto other shady groups with the secrets of making Mewtwo), I wonder if a "natural" Mewtwo is possible. A few times we've seen there being two Mewtwo's who existed prior to when it was possible to make a Mewtwo: Pokemon Conquest & Pokemon Ranger: Guardian Signs. So I'm wondering whether a Mew's transformation into a Mewtwo isn't just its evolution trigger malfunctioning. Remember that Mew is suppose to have the ability to evolve into different Pokemon, this evolution usually occurring for various reasons which dictates how the Mew should change. But what if this evolution process suddenly activated without any of those reasons, it just malfunctioned and told Mew to evolve? What would Mew evolve into? My guess is that Mewtwo is the result of the evolution trigger malfunctioning, evolving Mew into a Super Mew. In recent times shady scientists cloned a Mew and then discovered a way to activate this trigger, thus they think they made a new Pokemon.
Legendary Beasts: Super rare. Just because the most well known ones were created by Ho-oh when the Brass Tower burned down doesn't mean there aren't others. As just said, Ho-Oh created them so it probably has a way to create more. The Legendary Beasts are pretty much Ho-Oh's heralds and you'd probably want a few around just in case something happens to one of them. And with multiple of them existing, who says they aren't able to breed?
Ho-Oh & Lugia: Super rare. Like the Legendary Birds they're just very powerful Pokemon. So powerful that known ones are treated like deities, but that doesn't mean there isn't another Ho-Oh or Lugia somewhere else in the world.
Celebi: Due to Celebi's ability to time travel I don't think it can be said for certain whether there are different Celebi or all the Celebi are just ones from different points in time. If I were to pick one I'd say super rare, each major forest has its own Celebi, but there's only one in each forest and if you see anymore it's just the same Celebi from a different point in time. In addition I think all this time traveling has made Celebi immortal (or at least not able to age) so even if it does get captured EVENTUALLY whoever caught it will release it (whether because they only needed it temporarily to that person dying). Once released it'll go back to th point in time when it was caught and resume its duty of protecting its forest.
Legendary Golems: Super rare. Though made to seal away Regigigas, I wouldn't be surprised if more were made to assure they were "extra keys" lying around just incase Regigigas needed to wake up yet they can't find a set of Regis they made.
Eon Duo: Super rare. They're known to breed and the Soul Dew is a soul of a dead Latios/Latias. They're just very powerful Pokemon.
Weather Trio: One of a kind, sorta. Being incarnations of the land, sea, and air; though there's probably only one active at any time which can live indefinitely, if one to somehow die another would be created by its element (probably via an epic event) to maintain natural balance.
Jirachi: Super rare. They're just very powerful Pokemon who also enter thousand years hibernation which makes them even rarer. This is of course only for wild ones, but since they can naturally live thousands of years traveling with a trainer for a century isn't so bad and when its finally released it can go back to its thousand years sleep cycle.
Deoxys: Super rare. Just a powerful Pokemon who are from space. Heck, maybe they're only rare on the PokeEarth, maybe somewhere in the PokeUniverse there is a planet who's populated with variations of Deoxys. Sort of like a Space Mew (of course they would still have normal Mew's DNA in them).
Lake Guardians: Super rare. Though all are created from Arceus, since they're meant to have given the gift of emotions, knowledge, and willpower a considerable number of them were probably needed and placed all over the world and their power left to effect the inhabitants for possibly hundreds of thousands of years, if not millions. Being made by Arceus they're probably immortal.
Creation Trio: One of a kind, but more can be created if need be. They're essentially deities and they maintain time, space, and the Distortion World. They're pretty much indestructible, but even if one were to die somehow Arceus can simply create another. And being made from Arceus they're also immortal, and just because they're traveling around with a trainer doesn't mean they can't do their job as well.
Arceus: Super rare, sort of. Do you REALLY think you're capturing Arceus? Arceus is probably a massive universe-wide consciousness that has no definite form. Wat you're catching is just merely an avatar of Arceus, Arceus's chosen representation. The avatar has sort of its own consciousness but it knows its part of Arceus, yet it was made with a lower level consciousness to be able to interact with the beings living in its universe. The cosmic consciousness Arceus is busy maintaining the universe while the avatar Arceus are probably dealing with "smaller" tasks. And if one just so happens to get caught, no big deal, another could be easily created to take its place not to mention its immortal so eventually it'll get released.
Lunar Duo: Super rare. Just very powerful Pokemon.
Sea Guardians: Super rare. They're known to have eggs. Just very powerful Pokemon.
Heatran: Super rare. Just very powerful Pokemon. They even have defined genders.
Regigigas: Super rare. Not much is known about Regigigas except that it moved continents. Like the Legendary Golems, its possible it was created to do this task so more could have also been created. They shaped the Pokemon World and then a whole batch of Legendary Golems were created to seal them once their job was done. It's also likely it's immortal since it's essentially a living statue, an ancient robot.
Shaymin: Super rare. Just very powerful Pokemon.
Victini: Super rare. Just very powerful Pokemon.
Swords of Justice: One of a kind, sorta. I believe the Swords of Justice aren't born as they are but somehow transformed into what they are. They're the protector of Pokemon in the Unova region. And while one is probably only active at a time, if it were to die another Pokemon could be turned into one to replace it. In addition it seems like it's possible for new species to the Swords of Justice to be created, as evident by Keldeo. Keldeo of course was a very special case, but who knows if circumstances may come again and a fifth Swords of Justice could come into existence.
Forces of Nature: One of a kind, sorta. Like the Weather Trio, the Forces of Nature are incarnations of natural forces: Wind, Storms, and Fertility. If one were to die a new one would be created to take its place. They're likely to be immortal because of that. In addition, since they're more instigators of these forces rather then maintaining it, there's no problem with it traveling around with a trainer until they're released.
Tao Trio: Oh boy. I'm going to say one of a kind, sorta. Like Arceus I sort of see the Original Dragon not as a single being but a powerful consciousness that created an avatar. This Avatar sided with a king and when the king died it had to side with his sons. However each son wanted different things so not to be conflicted it split into 3 Pokemon: two sided with the sons while the other was what remained of the original dragon as it awaited for the time it can recombine. Eventually the ancient kingdoms the sons created fell and from it a unified Unova came into existence, however Reshiram and Zekrom became so much individuals they refused to fuse back with Kyurem and instead sought to continue the vision of the son they sided with. They're all immortal. Also since they really don't maintain any sort of natural balance there's no problem of them traveling around with a trainer.
Meloetta: Super rare. Just very powerful Pokemon.
Genesect: Going with super rare. We don't know how many Team Plasma created before N cancelled the project, and even then who's to say all the scientists stopped?
Mortality Duo: One of a kind, sorta. Like the Weather Trio and Forces of Nature, they represent a natural force: life and death. Infact they're almost impossible to kill because of that. Though I imagine if one were to perish another would be created by the force of nature it represents to maintain balance.
Zygarde: One of a kind, sorta. It shares a relation with the Mortality Duo which we'll probably see more of in XY2. Thus the same rule for those two apply for it.
Diancie: Super rare. Known to transform from a Carbink, there are probably a few Carbink kingdom with each having a Diancie queen.
(I'll hold my judgement about the other two Kalos Event Pokemon)
So yeah, pretty much my answer is that they're either super rare of if they're one of a kind another would be created if it was to die.