Many of the interactions and gifts require you to meet certain requirements, like it being a certain day.
Interactions
Red, Blue, Yellow:
Snorlax, Route 12, Route 16
Gold, Silver and Crystal:
Electrode x3, Mahogany Team Rocket Hideout
Shiny Gyarados, Lake of Rage
Lapras, Union Cave
Snorlax, Vermillion City
Sudowoodo, Route 36
Ruby, Sapphire and Emerald:
Kecleons, Route 119, Route 120
Electrodes, Magma/Aqua Hideout
Voltorbs, New Mauville
Sudowoodo, Battle Frontier. Emerald only
Firered and Leafgreen:
Hitmonchan/Hitmonlee, Saffron City
Lapras, Silph Co.
Eevee, Celadon City
Omanyte/Kabuto, Mt. Moon+Cinnabar Island
Aerodactyl, Pewter City+Cinnabar Island
Togepi, Water Labyrinth
Diamond, Pearl and Platinum:
Spiritomb, Route 209
Drifloons, Valley Windworks
Rotom, Old Chateau
Heartgold and Soulsilver:
Togepi, Violet City
Spearow, Goldenrod City
Eevee, Goldenrod City
Shuckle, Cianwood City
Tyrogue, Mt. Mortar
Dratini, Dragon's Den
Black and White:
Darmanitan, Desert Resort
Foongus, Route 6, Route 10
Amoongus, Route 10
Musharna, Dreamyard
Zoroark, Lostlorn Forest
Volcarona, Relic Castle
Black 2 and White 2:
Minccino, Route 5
Liepard, Route 5
Mandibuzz, Route 4
Braviary, Route 5
Volcarona, Relic Castle
Foonguses, Route 6
Crustle, Seaside Cave
Jellicent, Undella Bay
Shiny Haxorus, Nature Preserve
Omega Ruby and Alpha Sapphire:
Voltorbs, New Mauville
Kecleon, Route 119, Route 120, Lavaridge Town, Mossdeep City
Electrodes, Magma/Aqua Hideout
Spiritomb, Sea Mauville
Gifts
Red, Blue and Yellow:
Aerodactyl, Pewter Museum
Magikarp, Magikarp Salesman on Route 4
Omanyte/Kabuto, Mt. Moon+Cinnabar Island
Hitmonchan/Hitmonlee, Saffron City
Eevee, Celadon City
Lapras, Silph Co.
Gold, Silver and Crystal:
Togepi, Violet City
Pichu/Cleffa/Igglybuff/Tyrogue/Smoochum/Magby/Elekid, Day Care Centre
Spearow, Goldenrod City
Eevee, Goldenrod City
Shuckle, Cianwood City
Dratini, Dragon's Den
Tyrogue, Mt. Mortar
Ruby, Sapphire and Emerald:
Wynaut, Lavaridge Town
Castform, Weather Institute
Beldum, Mossdeep City
Firered and Leafgreen:
Aerodactyl, Pewter Museum
Magikarp, Magikarp Salesman on Route 4
Omanyte/Kabuto, Mt. Moon+Cinnabar Island
Eevee, Celadon City
Hitmonchan/Hitmonlee, Saffron City
Lapras, Silph Co.
Togepi, Water Labyrinth
Diamond, Pearl and Platinum:
Togepi, Eterna City
Eevee, Hearthome City
Happiny, Hearthome City
Porygon, Veilstone City. Platinum only
Riolu, Iron Island
Heartgold and Soulsilver:
Togepi, Violet City
Spearow, Goldenrod City
Eevee, Goldenrod City
Shuckle, Cianwood City
Dratini, Dragon's Den
Tyrogue, Mt. Mortar
Mareep/Wooper/Slugma, Violet City
Black and White:
Pansage/Pansear/Panpour, Dreamyard
Zorua, Castelia Ciry
Tirtouga,/Archen, Relic Castle+Nacrene City
Larvesta, Route 18
Omanyte/Kabuto/Aerodactyl/Lileep/Anorith/Cranidos/Shieldon, Twist Mountain+Nacrene City
Magikarp, Magikarp Salesman on Marvellous Bridge
Black 2 and White 2:
N's Zorua, Driftveil City
Deerling, Route 6
Eevee, Castelia City
Omanyte/Kabuto/Aerodactyl/Lileep/Anorith/Cranidos/Shieldon/Tirtouga/Archen, Join Avenue+Nacrene City
Magikarp, Magikarp Salesman on Marvellous Bridge
Happiny, Nacrene City
Tirtouga/Archen, Nacrene City
Omanyte/Kabuto/Aerodactyl/Lileep/Anorith/Cranidos/Shieldon, Twist Mountain+Nacrene City
Shiny Dratini/Shiny Gible, Floccesy Town
X and Y:
Tyrunt/Amaura, Glittering Cave+Ambrette Town
Lucario, Tower of Mastery
Lapras, Route 12
Omega Ruby and Alpha Sapphire:
Cosplay Pikachu, any Contest Spectacular building
Wynaut, Lavaridge Town
Castform, Weather Institute
Togepi, Lavaridge Town
Beldum, Mossdeep City
Camurupt, Battle Resort
Sharpedo, Battle Resort
Sources: Bulbapedia and Serebi's pages on interactable Pokemon (example)
