To help you out, we've put together a complete guide to finding these mythological 'mons, with a little help from Serebii and Kotaku.
Before you head off, you should take with you some Pokemon that cause satsu effects (making a Pokemon sleep or paralysing it greatly increases the efficacy of Pokeballs), and perhaps moves like Arena Trap (stops Pokemon escaping) and False Swipe (leaves 1 HP if you're about to knock out a critter).
Oh, and don't forget a big sack of Ultra Balls. And get the Master Ball from Team Magma or Aqua's hideout (depending on your version of the game) for Deoxys.
How to catch Kyogre and Groudon
These guys are part of the main story. Just before the final gym you'll be sent into the Cave of Origin where you'll battle these big beasties, and they'll be in their new primal form.
There's only one in your copy of the game. Big ground beasty Groudon is exclusive to Omega Ruby while water monster Kyogre is just for Alpha Sapphire players. If you want both, you'll need to trade with someone generous or gullible.
Both are level 45 so take some appropriately powerful team members.
How to catch Rayquaza and Deoxys
These guys are both part of the Delta Episode, which is an epilogue that activates after your beat the Elite Four.
Towards the end of this short story, you'll be sent off to capture Rayquaza - a badass level 70 dragon and flying monster. You have to capture this one to proceed (and you'll also be forced to shove it in your party for the time being).
Then, you'll fly off into space and and can battle Deoxys. At level 80, this psychic legendary is the highest level wild Pokemon in the game so you will probably want to use your Master Ball on this dude.
How to catch Latias and Latios
More legendary monsters that come as part of the main campaign. You'll get one of these guys - the blue Latios in Ruby and the red Latias in Sapphire, just to confuse things - by a chap called Steven.
They're level 30 but you're just given one, so you don't need to battle it. You'll have to trade if you want both of these soaring dragon and psychic monsters on your team.
How to catch Heatran
Heatran is a nifty fire and steel critter who can be found hanging out at the bottom (the third basement floor) of a location called the "Scorched Slab," just after you capture Groudon or Kyogre.
You'll discover a floating portal doodad which transports you into battle with a level 50 Heatran. Beat it down, put it to sleep, and stuff it into a tiny ball no bigger than a grapefruit.
How to catch the Regis and Regigigas
Okay, these dudes are a pain. You'll need the moves Surf, Dive, Dig, Strength, and Fly, and you'll need a Relicanth and a Wailord on your team. Once you've got all that, read on.
Start by going to Route 133 and then head west to get to Route 134. This is a stretch of water where strong currents carry you, and your surfing Pokemon, over to the west but if you follow the right path - taking the currents from island to island - you'll end up in a patch of deep, dark water that you can use the move dive in.
If you miss it, fly back to Route 133 and try again.
If you're in the right spot you'll descend into a secret cave. Head to the south of this area and you'll find some Braille on the wall (it says "Go up here"). Then go into the room below and use Dive again to ride back to the surface and enter the Sealed Chamber.
Find the Braille inscription at the North of the tunnel that translates to DIG HERE and use the move Dig. This will open a door. Inside, make sure Relicanth is the first Pokémon in your party and Wailord as is the sixth and then read the message at the end of the tunnel.
This will cause three earthquakes to trigger, opening passages on three routes that will take us to Regice, Regirock, and Registeel.
Regirock is at the bottom of the desert in Route 111, in a new location called Desert Tomb. Find the inscription with your instructions than walk right twice, down twice, and then use Strength. The door to level 40 rock monster Regirock will open.
Regice can be found in the Island Cave, which is on Route 105 in the west (you'll need to surf to find it). Inside is a Braille message telling you to wait so you need to sit around for two minutes before you can fight level 40 ice jerk Regice.
(Oh, and give this guy a nickname after you capture it, so you're ready for Regigigas).
Finally, Registeel is in the Ancient Tomb to the west of Lilycove on Route 120. Use fly in the middle of the room to solve the puzzle and get access to this level 40 steel critter.
Finally, for Regigigas we need to go back to the Island Cave with all three Regis in our party, but with some changes as explained by a girl in Pacifidlog Town. Basically, Regice needs a nickname and must be holding either a CasteliaCone, Snowball or Never-Melt Ice.
Now when you enter the Island Cave you'll fight the level 50 normal monster Regigagas. He's a very adaptable Pokemon that learns moves of all sorts of different types.
How to catch Ho-oh and Lugia
Okay, so you've dealt with Primal Groudon or Kyogre. And you have access to the Sea Mauville ship wreck. Awesome, dive in and swim to the very basement and then hammer the A button until you find a hidden item called the scanner.
Take this to Captain Stern in Slateport City and he'll give you a Clear Bell if you're playing Omega Ruby or the Tidal Bell if you're more of an Alpha Sapphire person. Take the bell back to Sea Mauville and they will start to resonate.
Head to top deck in Omega Ruby and Ho-Oh - a level 50 fire and flying monster - will appear. Or go to the underwater basement in Alpha Sapphire and Lugia - the level 50 psychic and flying legendary - will pop up for a brawl.
How to catch Raikou, Entei, and Suicune
These legendary dogs can only be found after you have both Lugia and Ho-Oh in your team, so you'll need to do some trading between versions.
Anyway, go Soaring in the Sky, and fly east of Rustboro City to find a new area (a "Mirage Spot") that looks like a small forest. Here you will find Raikou (electric), Entei,(fire) or Suicune (water). They're all level 50.
Says Serebii, you need to "remove the Pokémon from your team and then add them again to get the next" legendary dog on your return trip to this area. Well okay then.
How to catch Cobalion, Terrakion, and Virizion
Go back into the sky and soar around Pacifidlog Town to discover a large island called the Pathless Plain. Land and take a path to a peninsula that contains a portal.
Interact with the portal and a level 50 Virizion (grass and fighting), Terrakion, (rock and fighting) or Cobalion (steel and fighting) will challenge you.
According to Serebii you need a Pokémon with max effort values on your team for this area to appear, and you'll need to wait 12 hours before you can go back to the Pathless Plain and face another of these critters.
How to catch Uxie, Mesprit, and Azelf
Soar around Sootopolis City to discover the Nameless Cavern. Inside the cave is a portal which makes the level 50 Pokemon Uxie, Mesprit, or Azelf challenge you.
According to Serebii, you'll have to come back after 12 hours to battle a different one. And you may need a critter on your team with high happiness for this legendary encounter.
How to catch Palkia, Dialga, and Giratina
Once you have Azelf, Uxie, and Mesprit on your team, go Soaring in the Sky near Dewford Town.
You will discover a weird tear in the sky. Fly into it and a Palkia (water) will attack you in Omega Ruby, while a Dialga (steel and dragon) will set upon you in Alpha Sapphire. Both are level 50.
Get both on your team, (so you'll need to some cross-game trading), and return to this area and that tear in the sky will reappear. Enter to challenge a level 50 ghost and dragon critter called Giratina.
How to catch Reshiram, Zekrom, and Kyurem
The Black and White legendaries are caught in a similar fashion. Go Sparing near Mauville City to find an area with a star above it (Serebii says you need to have a Level 100 Pokémon on your team). This is the Fabled Cave which contains a portal.
Activate this portal and you'll encounter a level 50 Reshiram (dragon and fire) in Omega Ruby and Zekrom (dragon and electric) in Alpha Sapphire. Trade them onto the same game, chuck them on your team, and go Soaring in the Sky.
Now you'll find a new area near Fallarbor Town and Mt. Chimney called the Gnarled Den. Inside you'll find a portal that takes you to a level 50 dragon and ice monster known to his buddies as Kyurem.
How to catch Tornadus, Thundurus and Landorus
To get these guys, you'll need to have a Castform - an artificial Pokemon obtained in Weather Research Institute - on your team. Now go Soaring in the Sky to find a thunder cloud will over Fortree City.
Get close to it and you'll be able to encounter a level 50 Tornadus (flying) in Omega Ruby or Thundurus (flying and electric) in Alpha Sapphire. Once again, get them both and have them on your team.
Now go back to that thunder cloud to fight - and hopefully capture - the level 50 ground and flying monster Landorus.
How to catch Cresselia
And finally, there's Cresselia. But even the Pokemon experts at Serebii can't help us here. Somehow - the unlock method is still unknown - an island will appear south of Ever Grande City with a portal that gives you access to Cresselia. This is a level 50 psychic monster.