Before you start reading, let me get this out of the way.
Mythical Pokémon that cannot be obtained with event items: Jirachi, Phione, Keldeo, Meloetta, Genesect, Diancie, Hoopa, Volcanion, and Zeraora.
Also:
Meltan will begin to appear once a Mystery Box is opened in Pokémon GO, but be careful—they'll only appear for the player that opened the Mystery Box. Touch a Meltan you see on the field map, and then try to catch it with a Poké Ball! You can then bring the Meltan you catch in Pokémon GO to Pokémon Let's Go, Pikachu!/Pokémon Let's Go Eevee!.
With that out of the way, you can start reading.
Generation 2
Crystal: The Egg Ticket (Odd Egg) and the GS Ball (Celebi).
Generation 3
Ruby: The Eon Ticket (Latios).
Sapphire: The Eon Ticket (Latias).
Emerald: The AuroraTicket (Deoxys), the Eon Ticket (Latias/Latios), the MysticTicket (Ho-Oh & Lugia), and the Old Sea Map (Mew).
Fire Red: The AuroraTicket (Deoxys), the Eon Ticket (no event), and the MysticTicket (Ho-Oh & Lugia).
Leaf Green: The AuroraTicket (Deoxys), the Eon Ticket (no event), and the MysticTicket (Ho-Oh & Lugia)
Generation 4
Diamond: The Azure Flute (Arceus), the Member Card (Darkrai), Oak's Letter (Shaymin).
Pearl: The Azure Flute (Arceus), the Member Card (Darkrai), Oak's Letter (Shaymin).
Platinum: The Azure Flute (Arceus), the Member Card (Darkrai), Oak's Letter (Shaymin), the Secret Key (Rotom).
Heart Gold: The Azure Flute (no event), the Enigma Stone (Latios), the Lock Capsule (has no use), the Secret Key (no event).
Soul Silver: The Azure Flute (no event), the Enigma Stone (Latias), the Lock Capsule (has no use), the Secret Key (no event).
Generation 5
Black: The Azure Flute (no event), the Enigma Stone (no event), the Lock Capsule (TM95 Snarl), the Liberty Pass (Victini).
White: The Azure Flute (no event), the Enigma Stone (no event), the Lock Capsule (TM95 Snarl), the Liberty Pass (Victini).
Generation 6
X: the Discount Coupon (Used at any boutique for a one-time 50% discount).
Y: the Discount Coupon (Used at any boutique for a one-time 50% discount).
Omega Ruby: the Discount Coupon (Used at any boutique for a one-time 50% discount) and the Eon Ticket (Latias).
Alpha Sapphire: the Discount Coupon (Used at any boutique for a one-time 50% discount) and the Eon Ticket (Latios).
Generation 7
Prior to Pokémon Ultra Sun and Ultra Moon's release, certain Mega Stones and Z-Crystals were only obtainable through event distributions.
Official Megearna event QR code (SM/USUM):
(This is also worth mentioning) Pikachu Partner Cap QR code (USUM):
This is official, but it just isn’t on Pokemon.com.
Generation 8
(Sword/Shield)
After capturing Cobalion, Terrakion, and Virizion, a pair of brown
footprints will appear near a pot on an island in Ballimere Lake.
After interacting with the footprints and making a curry with
Cobalion, Terrakion, and Virizon in the party, Keldeo will appear on
the island.
Spin-offs
Pokémon Ranger: There are no items but, there is a code for a Manaphy egg and it still works: P8M2-9D6F-43H7
(the Manaphy can be transfered to the main series games).
Pokémon Ranch: here are steps to get Mew:
1. (if you don't already have it) Download My Pokemon Ranch
2. Open My Pokemon Ranch
3. Press 'Connect to DS' on ranch HUD.
4. Turn on either Pokemon Diamond or Pokemon Pearl.
5 On the DS, press 'Connect to Wii'.
6. Press 'Deposit All' to deposit all Pokemon from one box faster.
7. Deposit all Pokemon you have collected until you reach 1000 Pokemon.
8. Collect a Mew from Hayley in return for any random egg.
Sources
Source (Mew)
Source (Manaphy Egg)
Source (event items)
Source (Megearna & Pikachu Partner Cap QR codes)
Source (Meltan)