The Big Bang Theory episode The Codpiece Topology
September 29, 2008
The second episode of season 2 is about Leonard dating Leslie Winkle, forcing Sheldon out of the apartment while he's in with her, and some scenes reference Super Mario 64.
Near the beginning of the episode Sheldon reveals that his mother sent him his old Nintendo 64 with three controllers, a memory card and some games and his plan is to "rock Mario old-school!" with Leonard, but he's instead forced to play it on a Nintendo 64 emulator on his laptop on the staircase. Here he's met by Penny and after their dialogue he references the game by saying:
Everybody has a date. Even you Mario going after Princess Peach. And what am I doing? I'm just enabling you.
Later he also says:
Oh Mario, if only I could control everyone the way I control you. Hop, you little plumber, hop, hop, hop!
The only sound heard taken directly from the game is the pause sound, heard when Sheldon pauses the game to look at Penny while talking with her.
The Big Bang Theory episode The Electric Can Opener Fluctuation
September 21, 2009
In the first episode of season 3, all four main characters sport a beard and long hair after returning from three months in the Artic. Later they shave, but Howard keeps a mustache. He says: I call it "the Clooney", supposedly referencing George Clooney's mustached look while filming The Men Who Stare at Goats, to which Raj repies: I call it "the Mario and Luigi", but whatever.
The Big Bang Theory episode The Gorilla Experiment
December 07, 2009
In the tenth episode of season 3 Raj and Sheldon are seen playing Mario Kart Wii with the Wii Wheel and specifically Mario Circuit with Shaldon as player 1 using Mario on a bike and Raj as player 2 using Yoshi on a kart. After Raj wins he points out Sheldon's lack of skill:
Raj: Ha! Eat my dust, racially stereotypical plumber.
Sheldon: That’s not fair. I got stuck behind a tree.
Raj: And a cow and a penguin. Face it dude, whether it’s a real car or a virtual cartoon car, you can’t drive.
Sheldon: Just need a little more practice.
Raj: What you need is cheat codes, motor skills and a magic genie who grants wishes to little boys who suck at Mario Kart.
Note that cows are only featured in Moo Moo Meadows and penguins are only in Sherbet Land, so it's assumed they also played those levels and Sheldon used the same excuse.
The Big Bang Theory episode The Bozeman Reaction
January 18, 2010
In the thirteenth episode of season 3, the main characters' apartment got burglerized. After Leonard and Sheldon call the police, Sheldon lists to an officer all the things they took, including many videogames, three of which are Mario games, specifically: Super Mario Brothers, Super Mario Galaxy and Mario and Sonic at the Winter Olympics. Note that apparently robbers didn't take Super Mario 64 and Mario Kart Wii, the only two Mario games shown in previous episodes. Also a minor note is that Sheldon miscalled the last game "Winter Olympics", while is actually called "Olympic Winter Games".
The Big Bang Theory episode The Staircase Implementation
May 17, 2010
In a scene in the twenty-second episode of season 3, Raj, Howard, and Leonard are seen playing a Nintendo GameCube game on the couch. The sounds emitted from the TV tell that they are playing Mario Kart: Double Dash!!, and the music indicates that they are racing in Waluigi Stadium or Wario Colosseum.
The Big Bang Theory episode The Launch Acceleration
May 03, 2012
In the twenty-third episode of season 5, during a date between Sheldon and Amy at her house, she puts on a "romantic dinner music", that turns out to be the Super Mario Bros. theme. After hearing it, Sheldon admits that playing the game was the happiest 600 hours of his childhood.
The Big Bang Theory episode The Itchy Brain Simulation
May 17, 2010
The eight episode of Season 7 (Episode #143) features a reference to the Super Mario Bros. movie.
The Big Bang Theory company Warner Bros. had no rights over Nintendo's property, but they only included minor references to Mario.