I'll start with the Kanto Legendaries.

Zapdos

The Legendary Bird of Lightning. One of the Legendary Birds. I know of three of them off of the top of my head. One sticks to the Power Plant in Kanto, that you have to surf to near Mount Moon. Basically a Thunderbird. Can communicate with electric types by electrocuting each other. More info is known of the Titans. Has the worst attitude of the three.

Moltres

The Legendary Bird of Fire. One of the Legendary Birds. I know of four them. One in I think it's called Mount Ember? That one is on the 1,2, or 3 island in Kanto, which you can't get to until almost the end when you start to challenge the Elite four. One's in Mount Silver. The third is the Titan. A Firebird, though different from Ho-oh.

Arcticuno

The Legendary Bird of Ice. The final one of the Legendary Birds. I think there's at least four, one stays at the bottom of the Seafoam Islands. One I think is somewhere in the mountains between Kanto and Johto.


Titans

"Disturb not the harmony of fire, ice or lightning, lest these titans wreak destruction upon the world in which they clash. Though the water's great guardian shall arise to quell the fighting, alone its song will fail, lest the earth shall turn to ash. O Chosen One, into thine hands bring together all three. Their treasures combined tame the Beast of the Sea." Direct quote from the English version of the movie.

A very specific set of the Legendary Birds. The Titans of Fire, Ice, and Lightning. Seen in the second movie. They control the weather, when disturbed it has massive consequences. They do not leave their Islands. They're connected to orbs on the islands, possibly Aura is used on the orbs. When they're disturbed they fight, and the only thing that calms them is the orbs being activated, moved to a shrine on a fourth island, and Lugia's song being played on an ocarnia.

Mew

There's at least two of them. Shapeshifter, and said to be the ancestor of all Pokemon. Playful, much like a kitten, but can easily get into trouble. The first one was seen on New Island getting into a fight with Mewtwo, caused by Mewtwo. The second one has a symbiotic relationship with the Tree of Beginning in Kanto. The Tree of Beginning is guarded by a set of Golems. If the tree gets damaged, it's immune system starts to work, but it can also be killed. If either die, they both die. An infusion of Aura can save both Mew and the Tree, but the effort will kill. Lucario and the Mystery of Mew showed the Tree of Beginning, and it was caused by Mew's playfulness kidnapping Ash's Pikachu, so they had to try ad get him back, unfortunately damaging the Tree in their efforts.

Mewtwo

The final Kanto Legendary. A clone of Mew, said to be the strongest Pokemon in the world, though I'm pretty sure that Arceus would could flatten him if he wanted to. Created by Team Rocket, though the where depends on if you use the game or anime lore. New Island was where he was created in the anime, and no, the one with Genesect does not count.

Does not like humans, and with good reason. Was under Giovanni's care, for a time. Eventually escaped when he realized that he was being used by Giovanni. I tend to use the anime canon for him. Tried to destroy the world via a massive storm to wipe out everything but him and the clones of other Pokemon that he made, and was stopped when Ash stepped between him and Mew during their fight and sacrificed himself. He realized then that not all humans were bad, dissipated the storm, and flew off with the clones after mind wiping everyone there of his existence and returning the humans and their Pokemon to the mainland. Later in Johto he was living with the other clones on the top of a mountain, but he forgot to mind wipe Giovanni. Giovanni tried to recapture him, threatened the other clones, and he tried to sacrifice himself to save them. Ash saved him again, so he mind wiped Giovanni, but not Ash and co. He and the clones left the mountain top, with Mewtwo going to a city somewhere with a cloak on to become a vigilante and redeem himself.

Now for the Johto Legendaries.

Lugia

The Master of the Bird Trio. The Water's Great Guardian. At least four of them are known. Most info is known from the second movie. He keeps the current around the Titan's islands working correctly, and to smack the Titans down when they get out of hand. The current is the Beast of the Sea, not Lugia. He can't win against the Titans if they gang up on him. He's healed by his Song being played on the ocarina. He knows when to ask for help. Lugia is said to be able to cause a 40 day storm with a flap of it's wings. It is rumored to appear during storms. Fiercely protective of it's young. It's one of the Tower Duo along with Ho-Oh, though I can't remember which Tower burned down.

Ho-Oh

The Master of the Beast Trio. Guardian of the Skies. Something to do with the Towers in Johto. There used to be two towers in Johto, each connected to Lugia or Ho-Oh. One of them burned down in a storm, and three Pokemon died. Ho-Oh created the Legendary Beasts from the dead Pokemon. A Phoenix, though an Eastern one. It has an exclusive item called Sacred Ash, that works like a max revive, though much rarer and much more powerful. It is said to create rainbows as it flies, and there's proof in the very first episode of the anime. If Lugia is the storm, then Ho-Oh is the rainbow after the storm.

The Beasts. All of them tend to roam.

Entei

The Volcano Pokemon. The first Entei was born when Ho-Oh resurrected it after the Brass Tower burned. Lore wise they've been known to be born when volcanoes erupt, but it has to be a very big eruption for it to happen. Very strong fire, like magma strong.

One was born when Cinnabar Island erupted, and helped the land heal faster? That Entei ended up with Blaine I believe, though I could be remembering a fanfic I read.

Suicune

Suicune appears more often then the other Beasts. The North Wind. It can walk on water, and it purifies the water as it does so. Suicune appears to trust humans the most out of the three, but like all Legendaries you have to earn it.

Raikou

Out of all the Beasts, Raikou appears the least. It's the fastest of the three. Possibly able to fly? I don't know much about Raikou. Seems to distrust humans more than the other Beasts.

Celebi

Celebi can time travel, and uses it as a defensive measure. There's at least two, and a hoard of them appeared in the fourth movie to resurrect the one. The Voice of the Forest. It can heal plants, other Pokemon, and people. It can also purify Shadow Pokemon. It is a very peaceful Pokemon, and will not appear unless things are peaceful. Seems to make sure that things are on the right track, and will use it's abilities to ensure it.

Now for Hoen.

Golems

Created by Regigigas. Multiple sets. They do not seems to be very separate. They guard ruins and the like. Regirock, Regice, and Registeel. There's alse Regieleki and Regidrago, but those were introduced in gen VIII.

Jirachi

The Wishmaster. There's two of them I think. One of them is very powerful, and hibernates for most of a millennium, only waking for about a week during the fly by of a certain comet. Jirachi grants wishes, similar to Unknown. It has three eyes, and looks like a crystal or rock when hibernating. It can't make something out of nothing, it teleports the things to it instead.

Eon Duo

They are able to breed, and have been seen in large flocks. They tend to stay near water, can fly fast enough to break the sound barrier, can turn invisible, and can appear to shapeshift. They have slightly different stats and move sets between genders.

Latias

The female. Has been known to create illusions to look human. Latias is better at defense. Tends to be shy, but playful.

Latios

The male. Better at offense, has not been seen to "shapeshift". Seems to be more aggressive, and less trusting.

Deoxys

The space alien. There's at least two of them. Possibly guards the Pokemon world from otherworldly threats, does not come to the planet often, rides inside meteors occasionally. Gets into fights with Rayquaza if it comes into the atmosphere.

The Weather Trio

The Weather Trio are the main Legendaries of Hoen. This is where this get serious. Anything to do with Primal Reversion or Mega Evolution is from the remakes. Still gives a lot more lore points.

Kyogre

Kyogre created the seas. Can get into fights with Groudon when disturbed. The Red Orb can control it, but the Blue Orb can empower it, causing it to go into Primal Reversion. That form can cause it to rain endlessly, which will eventually flood the whole planet.

Groudon

Created the continents. Can get into fights with Kyogre. The Blue Orb can control it, the Red Orb causes Primal Reversion. The Primal Form causes a drought, left unchecked long enough the seas will dry up.

Rayquaza

Rayquaza stops Kyogre and Groudon's fights. Rayquaza also prevents the world from destruction of extraterrestrial threats, namely meteors. In the remake, Rayquaza swallowed a meteorite to go into Mega Form, fly up to the edge of the atmosphere, and destroyed a meteor that was about to hit the planet. Then Deoxys came out of the meteor, so their fights might be mistaken identity on Rayquaza's end, and self defense on Deoxys' end.

Time for Sinnoh.

Heatran

I know the least of Heatran when it comes to the Sinnoh Legendaries. They tend to live in volcanoes, and can cause them to erupt to not erupt.

Shaymin

Shaymin live in large groups, likely are able to breed. With the use of a Gracidea flower, they can switch forms and fly. They can absorb toxins and spit them back out as a powerful attack, the more potent/numerous the toxin, the stronger the attack. That also purifies things.

Regigigas

Regigigas created the Golems, and is their master. Regigigas also moved the continents into their current positions, and can hold back a glacier. The only way to find it is by collecting the other Golems and going to it's temple or shrine, which is always in the far north, possibly close to a Regice shrine.

Lunar Duo

Darkrai

Darkrai causes nightmares, just by existing. There's at least three of them. They can't control the nightmares that they cause, so they avoid other Pokemon and people. They will also cause nightmares to warn people of danger. The nightmares won't end without either Darkrai ending them, or Cresselia's help. You can't wake up.

Cresselia

The other half of the Lunar Duo. Cresselia can reverse Darkrai's nightmares, and wake the victims up. Also pretty aloof, and much rarer than Darkrai, though I assume that any Pokemon Duos always exist as a duo.

Lake Guardians

The Lake Guardians are one of the most important Trios there is. They are needed, for without them there's no Knowledge, Emotion, or Willpower. The Red Chain is created from their gems, which can control Palkia and Dialga. You need all of the Lake Guardians to make the Red Chain.

Uxie

The Being of Knowledge. Uxie was created by Acreus, without it, there's no knowledge. It sticks to Lake Acutiy in the Sinnoh region, in a cavern below the lake. It can teleport, use astral projection, and if you see it's eyes your memory is erased.

Mesprit

The Being of Emotion. Created by Arceus, without it there's no emotion. Touch it, and all of your emotions are drained away. Playful. Sticks to the underground cave in Lake Verity, but will also roam as opposed to the other Lake Guardians.

Azelf

The Being of Willpower. If Azelf is harmed, it can cause humans to lose all willpower, much like the victims of a Dementor's Kiss. Cautious, but can be bold when threatened.