My favourite easter egg is the special encounter with the Guardian of Forever in Fallout 2.
Not only is this a reference to the famous Star Trek original series episode "City on the Edge of Forever", but it actually connects together Fallout 1 and 2 in a mindblowing way!
In Fallout 1 you, the Vault Dweller, are searching for a new water chip for Vault 13 after their own chip broke. This is the whole motivation that sets off the entire series of games... but why did that chip break in the first place? You are led to believe that it was just normal wear and tear, but this is far from the truth.
In Fallout 2 the player is now the Chosen One, a grandchild of the original Vault Dweller, trying to save their tribal village by seeking a garden of Eden creation kit. This quest seems standalone, not strongly connected to the events of the first Fallout. But while the player is exploring the wasteland, they can came across a mysterious giant stone portal in the desert... the Guardian of Forever, which has the power of time travel! Entering this portal actually transports the player back in time, to a long-ago Vault 13, before the events of Fallout 1. After exploring the vault, the player finally finds a computer with a working water chip - and by tampering with it, causes the water chip to break before returning to the future!
This means that the entire quest of Fallout 1 was started by the player in Fallout 2! By breaking the water chip in the past, the Chosen One makes it necessary for the original Vault Dweller to leave the vault.
But hold on! The Chosen One is a grandchild of the Vault Dweller, and the only reason their tribal village exists in the first place is because the Vault Dweller traveled the wastes in Fallout 1 and was exiled from the vault...
So the quest of Fallout 1 only exists because of the Guardian of Forever in Fallout 2, and the quest in Fallout 2 only exists because of Fallout 1! This means that the entire storyline of both Fallouts 1 and 2 is one giant time travel paradox!
This is an ingenious easter egg, because it is a special encounter that can easily be missed by most players, but for those who find it it gives a whole new perspective to the plot. It also gives an interesting new view on the hero's journey of the main characters of Fallout 1 and 2: the Vault Dweller and the Chosen One are not just randomly chosen for their heroic paths, but rather they choose each other through a predestination paradox of time travel.