There are a lot of memorable easter eggs in games, from the secret room in Quake, to the corpse of the Space Marine from DOOM in Duke Nukem, but the one I liked the most was one from Portal 2.
In the area of the old Aperture Science facility, behind a closet is a door that leads to a hallway, at the end of which is a hatch that leads to an empty dock where a lifebuoy with the word BOREALIS can be seen. That ship is mentioned in Half-Life 2, which link both games in the same universe. I liked that detail.

Meet the devs in chrono

Earn up to 127 lives by kicking Koopa Shells repeatedly against staircases in Super Mario Bros., such as at the end of World 3-1. Unique!

I like the the Minecraft Easter Egg in Borderlands 2 where you can unlock a creeper head to wear to show you have done it. It’s simple but at the time I really liked it.

All G-Man Easter eggs during HL campaigns

In The Witcher 3, the FCK DRM Easter egg. Actually the was a lot of Easter eggs in the Witcher 3 from "Twilight" to "Tomb Raider" and even the "Star Wars" bounty hunter, Djenge Frett.

Fallout: New Vegas....Wild Wasteland....Indiana Jones skeleton in the fridge. I hated that scene in the 4th movie and seeing a joke of it in New Vegas was great.

Far Cry 4 secret; where at the start of the game; either you wait for Pagan Min or run out. If you decide to run; at the end of the game you can kill or spare Pagan Min.

Of course i love the bunny Daisy in Doom Eternal, cuteness in a world of violence ♥

Toejam & Earl the secret hulla island

It required having some specific presents (rocket skates were the best) and going back to the beginning of the game and finding the island. But it was so worthy, a small island, with free promotions and a hot tub with hulla dancers. A nice chill place before going back up all the floors.

My favourite easter egg is a very secret thing from the first Discworld adventure game - the first instance of the f-word being used in a videogame.

If you click on a series of semingly-random points on the screen in the final encounter, Rincewind (voiced by Eric Idle) will say "I want to be the first person in a game to say f*ck".

Runner-up being in the sequel, where it's a VERY low chance to occur in the portal to have a scene of Rincewind talking to himself from the first game and say "I want to be the very first person to say f*ck in a sequel". This easter egg was actually found FIRST, because of how hard it was to trigger in the first game, and was an approved secret by the publisher unlike the first game's (it's bleeped out, unlike the original)

I love easter eggs which spans across a series.
My favorite game series is Bioshock.
In the first game, when you arrives at Rapture, a splicer when sees the bathysphere, asks "is it someone new?"
In Bioshock Inifinte when you meet Preacher Witting, he asks the same question!

My favourite secret is the New World Computing Dungeon in Might and Magic VI: The Mandate of Heaven.

The dungeon contains a number of rooms that ressemble the company's offices of the time of the development of the game. And the monsters and characters in it are named after the developers.

One of my favorites is that in the first Ultima Underworld, you can find, "an upset ghost named Warren" floating around, referencing the game's producer, Warren Spector... but as a spectre.

Hahaha, that's great!
Reminds me of some old and probably obscure (text?) adventure that I played as a kid on my C-64.
At some point, I got so annoyed with the lack of understanding on side of the parser (permanently: "I don't know..."/"I don't understand..."), that I started typing in obscenities and insults.
The game registered that and reacted with stuff like "hey! Language!", "watch your tongue!", etc.
However, when you continued typing in that stuff (which I did, of course), it would warn you "I won't tolerate such behaviour any longer" etc.
If you then still continued, the game simply reset to the BASIC screen.
No "save game" [Y/N], no fucks given.
You didn't behave, so you got punished.
It was awesome.
:)