I'm discounting erratic behavior here such as summoning a L245 Mewtwo on Cinnabar Coast, or anything that involves getting a foothold to execute your own code.
Red, Japanese Green, International Blue
Wild Pokemon: L64 Chansey at Cerulean Cave, using a traded Pokemon without letting anyone else split the yield. 3497
Trainer Battle: Rival's L65 Blastoise in champion battle, using a traded Pokemon without letting anyone else split the yield. 4387 (note that the rival only has Blastoise if you picked Charmander; if he has Venusaur or Charizard instead, those are worth 4345 or 4366 respectively)
Japanese Blue
Wild Pokemon: L70 Mewtwo at Cerulean Cave, using a traded Pokemon without letting anyone else split the yield. 3300 (as Chansey only reaches level 56 in this game, where it's worth 3060)
Trainer Battle: Rival's Blastoise for 4387 as above
Yellow
Wild Pokemon: L70 Mewtwo for 3300 as above
Trainer Battle: Lance's L62 Dragonite in the Elite Four, using a traded Pokemon without letting anyone else split the yield. 4344
Gold, Silver (Starting in these games, the Lucky Egg was first available as a held item.)
Wild Pokemon: L70 Lugia at Whirl Islands (Gold), or L70 Ho-oh at Tin Tower (Silver), using a traded Pokemon holding Lucky Egg without letting anyone else split the yield. 4950
Trainer Battle: Mystery Gift with another game where the party includes a L100 Blissey, then battle that team at the Trainer House, using a traded Pokemon holding Lucky Egg without letting anyone else split the yield. 12291 (displays as a garbage character followed by "291" as seen here)
Crystal
Wild Pokemon: Either L60 Lugia or Ho-oh, as above except for the lower level. 4242
Trainer Battle: Trainer House Blissey for 12291 as above
Ruby, Sapphire, Emerald
Wild Pokemon: L70 Rayquaza at Sky Pillar, using a traded Pokemon holding Lucky Egg without letting anyone else split the yield. 4950
Trainer Battle: Mix records with another game where the party includes a L100 Blissey, then battle that team at a Secret Base, using a traded Pokemon holding Lucky Egg without letting anyone else split the yield. 12291
FireRed, LeafGreen
Wild Pokemon: Find a L67 Ditto at Cerulean Cave, get it to transform into your traded Blissey holding a Lucky Egg, and defeat Ditto without anyone else getting involved to split the yield. 5491 (Transform copies the target's experience yield in gen 3-4 games, but no others.)
Trainer Battle: Rival's L75 Blastoise in a champion battle rematch, using a traded Pokemon holding Lucky Egg without letting anyone else split the yield. 7593 (If the rival has Venusaur or Charizard instead, those are only worth 7521 or 7557 respectively, falling below the 7567 of his L72 Tyranitar.)
Diamond, Pearl (Starting in these games, Wi-Fi communication was first possible, and in particular long-distance trades, so Pokemon that were traded from a different country get an even bigger boost in experience than usual trades do.)
Wild Pokemon: Either L70 Giratina in Turnback Cave or L70 Regigigas at Snowpoint Temple, using an internationally traded Pokemon holding Lucky Egg without letting anyone else split the yield. 5610 (Using the "tweaking" glitch to navigate out of bounds to the scripted L80 Arceus encounter can do better than this, but that's excluded on the same grounds as R/B Cinnabar Coast nonsense, and the item that was supposed to unlock that battle normally was never legally released, not even as a time-limited event.)
Trainer Battle: Rival's L74 Empoleon in the Battle Zone rematch after you've taken care of the Heatran quest and beaten Cynthia at least 20 times (he can only be challenged there on Saturday or Sunday), using an internationally traded Pokemon holding Lucky Egg without letting anyone else split the yield. 8491 (If the rival has Torterra or Infernape instead, those are only worth 8410 or 8451 respectively.)
Platinum
Wild Pokemon: L70 Dialga or Palkia atop Mt. Coronet, using an internationally traded Pokemon holding Lucky Egg without letting anyone else split the yield. 5610
Trainer Battle: Rival's Empoleon as above, but this time it reaches L85. 9753 (If the rival has Torterra or Infernape instead, those are only worth 9660 or 9707 respectively.)
HeartGold, SoulSilver
Wild Pokemon: L70 Lugia (HeartGold, Whirl Islands), Ho-oh (Soul Silver, Bell Tower), or Mewtwo (either game, Cerulean Cave), using an internationally traded Pokemon holding Lucky Egg without letting anyone else split the yield. 5610
Trainer Battle: Red's L84 Blastoise atop Mt. Silver, using an internationally traded Pokemon holding Lucky Egg without letting anyone else split the yield. 9639
Black/White (These games tweaked the experience formula to include a scaling factor that depends on your level as well as theirs, which can provide significantly greater rewards if an underleveled Pokemon defeats an opponent, or reduces them to almost nothing if you're training against opponents far lower than your own level. They also introduce Pass Powers as a reward for inter-player communication which can, among other things, increase or decrease all experience gains for a temporary period.)
Wild Pokemon: L75 Kyurem at Giant Chasm, while Exp. Point Pass Power ↑↑↑ is in effect, using a level 1 internationally traded Pokemon holding Lucky Egg and without letting anyone split the experience (such as by switching to someone who can KO Kyurem with Explosion). 107264
Trainer Battle: Go to Big Stadium in Nimbasa City, hope to find Doctor Jules there randomly while Exp. Point Pass Power ↑↑↑ is in effect, and battle their L65 Audino using a level 1 internationally traded Pokemon holding Lucky Egg and without letting anyone split the experience (such as by switching to someone who can KO Audino with Explosion). 178632
Black 2, White 2
Wild Pokemon: L59 Audino at Route 18 or one of the other nearby postgame-only areas, while Exp. Point Pass Power ↑↑↑ is in effect, using a level 1 internationally traded Pokemon holding Lucky Egg and without letting anyone split the experience (such as by switching to someone who can KO Audino with Explosion). 100000 (There is a hard cap in these games, and the experience yield would otherwise reach 106117 in its absence.)
Trainer Battle: Any Pokemon Breeder's L82 Blissey in area 10 of White Treehollow in Challenge Mode, using a level 25 or lower internationally traded Pokemon holding Lucky Egg and without letting anyone split the experience (such as by switching to someone who can KO Blissey with Explosion). 100000 (would be 182615 without the cap if you were using a level 1 Pokemon, or up to double that with Pass Powers)
X, Y (Starting in these games, if multiple Pokemon received experience in the battle, they would all get the full amount instead of having to split it; the affection mechanic was introduced as another way to boost experience; Pokemon that evolve by reaching a specific level threshold would also receive a boost if they remained unevolved beyond that level; the scaling factor from the generation 5 formula temporarily went on hiatus; and if multiple Pokemon fainted at once, the experience from all of them would be handed out in a single consolidated message instead of multiple messages)
Wild Pokemon: Summon a horde of L29 Floatzel in Victory Road, while level 3 Exp. Point O-Power is in effect, letting an internationally traded Pokemon holding Lucky Egg, with an affection bonus, that evolves by level-up and is already past its natural evolution level be active at some point in the battle without fainting, and knock out all five Floatzel simultaneously with a single spread move. 21900
Trainer Battle: Have a Triple Battle Meal at Restaurant Le Wow in north Lumiose City while level 3 Exp. Point O-Power is in effect. During the second battle, against Amoonguss, Alomomola, and Audino all at L63, allow an internationally traded Pokemon holding Lucky Egg, with an affection bonus, that evolves by level-up and is already past its natural evolution level to become active at some point in the battle, and have your center-slot Pokemon knock out all three opponents simultaneously with a single spread move. 49362
Omega Ruby, Alpha Sapphire
Wild Pokemon: The L80 Deoxys either atop Sky Pillar or in space immediately after catching Rayquaza, while level 3 Exp. Point O-Power is in effect, letting an internationally traded Pokemon holding Lucky Egg, with an affection bonus, that evolves by level-up and is already past its natural evolution level be active at some point in the battle. 18878
Trainer Battle: Find a Secret Base partner whose team consists of three L100 Blisseys; challenge them while level 3 Exp. Point O-Power is in effect in a base with an activated Level Release machine and that's set up to allow Triple Battles as its format of choice; make sure an internationally traded Pokemon holding Lucky Egg, with an affection bonus, that evolves by level-up and is already past its natural evolution level gets to be active at some point in the battle; and knock out all three Blisseys simultaneously with a single spread move from your center slot. 239160
Sun, Moon (Starting in these games, there was no bonus experience for trainer battles relative to wild battles.)
Find a Dratini in Poni Gauntlet while Exp. Share is off, get it to SOS call for a L59 Dragonair, KO the Dratini, get Dragonair to SOS call for a L59 Dragonite, find some way to get a level 1 internationally traded Pokemon holding Lucky Egg and with an affection bonus into the battle safely while both of these opponents are out, and defeat both Dragonair and Dragonite simultaneously with a single spread move. 68069
Ultra Sun, Ultra Moon
Find a L57 Chansey at Poni Plains while Roto Exp. Points is in effect, get it to SOS call for a L57 Blissey, find some way to get a level 1 internationally traded Pokemon holding Lucky Egg and with an affection bonus into the battle safely while both of these opponents are out, and defeat both Chansey and Blissey simultaneously with the same spread move. 235654
Let's Go Pikachu, Let's Go Eevee
TBA
Sword, Shield
TBA
