Yars Revenge (Atari 2600)

Programmers: Destroy the Swirl in mid-air then stay on the lower-half of the solid vertical line during the explosion. The initials "HSWWSH" will appear, which is a reference to the game's programmer Howard Scott Warshaw.
Status: TRUE: Verified by FO. Note: The is the first "easter egg" I can ever remember discovering in a game. I didn't even know what it was way back when I first saw it happen. I didn't realize it was someone's initials and just assumed the game had glitched up.

Programmers: The Yar is "Ray" spelled backwards. The game takes place in the Razak Solar System. This is "Kassar" spelled backwards, and the double "s" replaced with a "z". These are a reference to Ray Kassar, who once worked for Atari. (Credit: Kairobi King)
Status: TRUE: Verified by FO. Numerous sources have confirmed this one.

Yoshi's Story (N64)

Cross-Series (Mario Paint): On the Story Select Screen, wait for the music to loop a few times. Kozumi Totaka's signature tune will play (the "Mario Paint tune"). (Credit: Mark Kelly)
Status: Unverified

Yu-Gi-Oh: World Championship 2004 (GBA)

Cross-Series (Goemon): There is a card called "Sasuke Samurai" that is definitely modeled off of Sasuke from the Goemon games. (Credit: MJB817)
Status: Unverified

Cross-Series (Gradius): There is card called "Gradius" which has a picture of the Vic Viper on it and is an obvious reference to the Gradius games. (Credit: MJB817)
Status: TRUE: Verified by FO. Source: www.classicgaming.com/gradius