Mass Effect - Did You Know Gaming? Feat. Really Freakin Clever
The Sims - Did You Know Gaming? Feat. Brutalmoose
According to Chris Priestly, Conrad Verner was almost cut from Mass Effect 2 and Mass Effect 3, but enough members from the development team wanted him to stay that he was kept in both games.
Contributed by ProtoSnake
During the "Tali: Treason" Loyalty Mission, Shepard is introduced to Admiral Zaal'Koris vas Qwib-Qwib, with the "vas Qwib-Qwib" part referring to the ship he lives in following his Pilgrimage away from the fleet. If Shepard further questions Zaal'Koris about the Qwib-Qwib and why he has not changed its name to something less embarrassing, he comments about possible alternative names like "the Defrahnz" or "the Iktomi". Spoiler:Putting those names next to the "vas" title creates the names "vas Defrahnz" and "vas Iktomi", referencing the vas deferens and the related term vasectomy respectively.

The Qwib-Qwib ship itself may also be a direct reference to the ship of the same name from Fred Saberhagen's science-fiction novel series Berserker.
Contributed by MehDeletingLater
Christina Norman, one of the designers for Mass Effect 2, increased enemy health and damage by 20% overall the day before the game was finalized without telling anyone.
Contributed by Psychospacecow
On the Citadel, the player can interract with a vending machine that dispenses a popular soft drink named Tupari. When interracted with, the machine will play a number of slogans promoting Tupari, one of which is "Tupari brings your ancestors back from the grave!"

This appears to be a reference to a popular advertising urban legend regarding the real life soft drink Pepsi, in which its Pepsi Generation slogan "Come alive! You're in the Pepsi Generation!" was supposedly misinterpreted in Chinese (or other Asian languages) as "Pepsi brings your ancestors back from the grave."
Contributed by MightyKombat
In Kasumi's DLC mission, the player at one point infiltrates Donovan Hock's vault, filled with various works of art. One particular piece is the head of the Statue of Liberty. When interracted with, Kasumi will say "Damn you, Hock!" This is likely a reference to Charlton Heston's character's breakdown at the end of the original "Planet of the Apes" movie.
Contributed by ghostkiller
At one point in the game the Shadow Broker will say "You travel with fascinating companions, doctor." This could be a reference to the TV Series "Doctor Who" Where the main character, known as The Doctor, often travels with many companions through time and space.
Contributed by Boyobmas
Speaking to Thane frequently will reveal that he and his son have a bad relationship. After his loyalty mission, they reconcile their differences. Upon finishing the mission, the player is rewarded with the achievement/trophy "Cats in the Cradle". This is a reference to a song of the same name by Harry Chapin, which is about his relationship with his son.
Contributed by FUS RO DAH
In the Lair Of the Shadow Broker, during the chase with Vasir, when going through the tunnels, a wanted poster for Jack (Subject Zero) can be seen.
Contributed by FUS RO DAH
Should the player allow time to run out during the Arrival DLC chapter, a special Game Over cutscene will play showing the Reapers' attack.
Contributed by FUS RO DAH
When in the Sol system, the player can launch probes at the planet Uranus. Doing so will also illicit one of two sarcastic responses from EDI:

"Probing Uranus."
"Really, Commander?"
Contributed by FUS RO DAH
It appears that originally the player could recruit Thane, Tali, Samara or Legion a lot earlier in the game; possibly directly after the prologue like Miranda and Jacob. By using an editor tool to unlock them from the beginning of the game, players will discover that the four have extensive dialogue for virtually every mission in the game, including missions which must be complete before their official recruitment missions. Furthermore, there are some unique scenes should the player bring Legion in particular along onto certain missions, such as characters commenting on his presence.

Legion's presence also triggers an exclusive Paragon Interrupt during Tali's recruitment mission. Upon meeting Tali, she will notice Legion and immediately draw her gun, triggering a Paragon Interrupt prompt. If the player doesn't press it, she will open fire at Legion who will run for cover.
When exploring Donovan Hock's vault in the DLC 'Kasumi: Stealing Memory', there is a statue of an ogre from the Dragon Age series; another game franchise created by BioWare.