I thought I'd compile a list of references to prior games in a post so that others could share ones that I may have missed. Seen as it's still relatively new there may be ones that we have missed. Some may even have lore implications whilst others exist purely as nods to other media of a 25 year running franchise. I'll try to keep away from aesthetic references which are part of most games (i.e Fancy Lad Snack Cakes) but I will reference game specific items (such as Sunset Sarsaparilla) or if the aesthetic is relevant to the reference.
Fallout 1:
- A reference to the Vault Dwellers Survival Guide in Vault 33 which contains a Pip Boy variant of Tim Cain (Thanks to another recent user for finding this one)
- A direct reference to the story with the Water Chip in Vault 33 breaking.
- The Obelisk and Water Well from Shady Sands endings is visible in a flashback in Episode 8
- Bakersfield is the only location mentioned that could be taken as a reference given it becomes Necropolis.
- Colt 10MM Pistol is quite prominently wielded by Maximus, Thaddeus and also by Lucy (more so than the N99)
- Vault 13 and Vault 15 are possibly visible on the Vault-Tec Vaults Map of the United States during the Corporate Meeting.
- Leon Von Felden of West-Tek
- General location of the show is set within the Los Angeles Boneyard
- Vault-Tec Headquarters in Los Angeles which appeared very briefly in the intro of Fallout 1.
- Brotherhood Ideology is more similar to that of the Classic Games
- Code for Moldaver's Cold Fusion is the original release date of Fallout 1 (October 10th 1997)
Fallout 2:
- Reference to the President being missing. An indirect reference to the Poseidon Oil Rig (Known as Control Station ENCLAVE)
- What looks like a Chrysalis Highwayman is partially visible in Episode 3 near the Gulper lake. Though it's unclear if it is one.
Fallout 3:
- Capitol Post newspaper can be seen during one of Cooper Howard's flashbacks
- The Enclave experiment with animal behaviour is reminiscent of their Deathclaw experiment from Raven Rock (itself carried over from the Oil Rig)
- Billboards and Propaganda Posters from Fallout 3
- Snip Snip the Mister Handy has orange tinted eyes which are reminiscent of the Fallout 3 and NV Mr Handy design.
- One of the Vault experiments proposed during the Corporate Meeting correlates well to Vault 106 and it's white noise experiment
- Another proposed experiment correlates to Vault 87 and the FEV experiment.
- Norm uses the hacking mini game first introduced in Fallout 3
Fallout New Vegas:
- Sunset Sarsaparilla billboards (Twice)
- NCR Veteran Ranger Combat Gear in Episode 7
- A reference to a character's mother's profession being that of a Courier
- Nuka Cola Victory (first appeared in New Vegas as a West Coast Exclusive)
- Robert House (Self-explanatory)
- REPCONN and Julia Masters at the Corporate Meeting
- BIG MT and Frederick Sinclair at the Corporate Meeting
- A sly dig by Robert House that Sinclair "Could Lose Money By Running A Casino". Perhaps an indirect reference to the Sierra Madre.
- a photograph of Aaron Kimball during the Flame Mother ceremony
- New Vegas itself appears in the end credits of episode 8 (Including the Lucky 38, The Tops, Gommorah and the Ultra-Luxe)
- End Credits of Episode 8 show NCR Vertibirds and soldiers wearing similar armour to their standard combat armour in the Mojave Campaign.
- Cannibalistic raiders known as the Fiends. Could just be a name reference but it works.
- NCR propoganda posters and Flag (New Vegas version of the flag) in Vault 4
Fallout 4:
- T-60 Power Armour is prominent within the show. Characters seem a little surprised by it's appearence. It's possible that it was specific to the East Coast
- The Prydwen appears in multiple episodes. Implying it's destruction in two of four endings in Fallout 4 never happened.
The Commonwealth is directly referenced in name by Elder Cleric Quintus
- Assault Rifle from Fallout 4 appears closer to it's original design indication as a machine gun for power armour
- Minutemen Radio makes a brief appearance in Episode 7
- Serum that transforms people into Ghouls is similar to what happened to John Hancock in Goodneighbour
- Cryogenic Facilities feature heavily in the show. It was prominent in Vault 111 showing that Vault-Tec had access to the technology.
- Atomic Command Holotape
- Junk Jet appears in Episode 1
- Broken Assaultron in Episode 2
- A variation of the Gulper appears in Episode 3
- General posters and propaganda that appeared in Fallout 4
Fallout 76:
- Pip Boy 2000 Mark VI appears in the window of Ma June's Sundry
- Lucy references Reclamation Day which we first saw in Appalachia
- One of the Vault Experiments proposed in the Corporate Meeting correlates well to Vault 51 and it's AI overseer experiment.
Other References:
- Elder Quintus mentions that the Brotherhood used to rule the Wasteland (Unknown if it's a reference to the West Coast Chapter, East Coast, Midwestern or all three)
- NCR founding information correlates roughly to the Fallout Bible such as it's founding date.
- Unintentional reference to the "Loser Walk" in Fallout 1 where NPC's have a specific walk and posture which a small character in the show imitated almost perfectly.
Sources:
Gamesradar
Fallout TV Show
IGN
JagoandLitefoot (User)
Reddit (r/Fallouttv) (r/Fallout)
Oxhorn
The Appalachian