August 11, 2000
Luigi's Diary in Paper Mario is a secret book found in Mario and Luigi's room, and after every chapter of the game a new page will be added for the player to read. Page 2 tells that Luigi is terrified by ghosts, while page 7 tells how much he would want to star in his own adventure. These are possible foreshadowing of his adventure in Luigi's Mansion, that was in development at the time.
As a side note, Luigi specifying "my name would have to be in the title" might be an aknowledgement of Mario is Missing! the first and at the time only game to star Luigi as the protagonist, but that wasn't titled after him.
September 14, 2001
Luigi's Mansion is an adventure game with horror themes starring Luigi, Mario's brother previously the secondary hero in the Mario series (with the only exception of the educational game Mario is Missing). Mario is here trapped in a painted by the ghosts and must be saved by his brother. Toad also appears in a supporting role, while the enemy roaster is composite almost exclusively by ghosts, and includes the Shy Guy Ghost, and fifty-one Boos, including King Boo, that debuts disguised in a mechanical Bowser suit.
Additionally the ghost character Melody Pianissima occasionally plays remixes of the underwater theme from Super Mario Bros. and of the grass stage theme from Super Mario Bros. 3.
Super Mario Sunshine
July 19, 2002
Professor E. Gadd from Luigi's Mansion is referenced in this game, After Mario finds F.L.U.D.D., it says: "Thank you for purchasing this item from Gadd Science, Inc." implying Professor E. Gadd from Luigi's Mansion to be the one who created it. What can be assumed to be the Gadd Science, Inc. logo, representing the Professor's head can be seen on the boxes for F.L.U.D.D.'s nozzle upgrades and on F.L.U.D.D. itself.
Also, Bowser Jr. later says that he got his Magic Paintbrush from "a strange old man in a white coat." That's confirmed to be Professor E. Gadd by the Gadd Science, Inc. logo that can be seen on the brush.
Worth mentioning is the boss character called King Boo, sometimes believed to be the same character from Luigi's Mansion, but since his original japanese name is Boss Boo (Bosu Teresa in Japanese), instead of King Boo (Kingu Teresa in Japanese), and his look is quite different, he can be assumed to be a different character.
Mario Party 4
October 21, 2002
The Gaddlight item is used to scare Boos away, referencing Luigi's Mansion. Given its name, it's supposedly created by Professor E. Gadd.
Mario Kart: Double Dash!!
November 07, 2003
King Boo is a playable character in Mario Kart: Double Dash!!, unlocked along with his partner Petey Piranha and the "Piranha Pipes" kart by obtaining a gold trophy in the Star Cup in Mirror Mode. Obtaining a gold trophy in the Special Cup in Mirror Mode unlocks his personal kart "Boo Pipes", a black recoloring of the "Piranha Pipes" kart.
King Boo later returns as a playable character in Kario Kart Wii.
The game also features a "Luigi's Mansion" battle course, unlocked by obtaining a gold trophy in the Mushroom Cup in 150cc Mode. It is depicted as a three floor maze, with the second floor based on the Ball Room from Luigi's Mansion.
Additionally, Luigi's "New" Mansion from the "Rank A" ending of Luigi's Mansion, can be seen in the background of the Luigi's Circuit stage.
Mario Party 5
November 10, 2003
Like the previous Mario Party game, this one features some of Gadd's inventions. The game features customizeable vehicles to use in Super Duel Mode, and some parts are named after the professor, being:
There also is a minigame called E. Gadd's garage, that was made into a full board in Mario Party 6.
Mario & Luigi: Superstar Saga
November 17, 2003
In the Starbeans Café, Professor E. Gadd makes an appearance every time a new coffee is mixed, and he gives one of his inventions o Mario and Luigi. Occasionally ghosts from Luigi's Mansion also appear and when they do, the main theme from Luigi's Mansion can be heard. In one occasion he also appears in "videoconference" trough a Game Boy Horror console originally from Luigi's Mansion.Note that originally every item obtained was given to Mario and Luigi by a different cameo character (Wario, Fox McCloud, a biker from Excitebike, Link, Samus Aran, Captain Olimar and Professor E. Gadd) but in the end the developers only retained Professor E. Gadd. The invention originally given by him was left unchanged and is a new version of the Game Boy Horror, called "Game Boy Horror SP", obviously based on the Game Boy Advance SP.
Paper Mario: The Thousand-Year Door
July 22, 2004
In Paper Mario: The Thousand-Year Door, Luigi sometimes makes an appearance in the audience during battles and he sometimes does with the Poltergust 3000 on his back.
Mario Power Tennis
October 28, 2004
The titular mansion from Luigi's Mansion is featured in Mario Power Tennis as a playable court. The match takes place in the courtyard and features cameos of various ghasts from the game.
The minigame "Terror Tennis" takes place in the Luigi's Mansion court and consists in fighting the ghosts from Luigi's Mansion by hitting them with the tennis ball to make them retreat in their portraits.
Additionaly, Luigi's Defensive Power Shot is called "Poltergust Return" and has him use the Poltergust 3000 t suck the tennis ball and then shoot it back out. He uses the same shot in Mario Tennis: Power Tour.
Super Mario 64 DS
November 21, 2004
In Super Mario 64 DS King Boo was added in Big Boo's Haunt as an optional boss that has to be defeated to unlock Luigi. In this game King Boo has trapped Luigi in a painting and Mario has to save him, swapping their roles from Luigi's Mansion. Defeating King Boo unlocks Luigi as a playable character.
The "Hide and Boo Seek" minigame in Super Mario 64 DS is also based on Luigi's Mansion and has Luigi trying to find all Boos in the mansion before time runs out. To do so the player has to rub the screen with the stilus. Oddly this is one of Yoshi's minigame, despite Luigi being the main character. Like most minigames, this one also returns in New Super Mario Bros.
Mario Party Advance
January 13, 2005
In the game the player can spend coins to buy Professor E. Gadd's Gaddgets. There's a total of eighty Gaddgets in the game.
The Professor also returns in Mario Party 5 and Mario Party 6.
Mario Superstar Baseball
July 21, 2005
King Boo appears as a playable character and a member of Wario's baseball team. He has bad chemestry with Luigi, referencing their rivalry from Luigi's Mansion.
He later returns in Mario Super Sluggers.
Mario Kart DS
November 14, 2005
The titular mansion from Luigi's Mansion is featured in Mario Kart DS as the last race course of the Mushroom Cup, with its appearance based on the game. It's also used during missions 1-6 and 2-4, with Luigi driving in both of them, referencing the game. This course returns in Mario Kart 7 as a classic course, with some minor differences.
Additionally, Luigi's "Poltergust 4000" kart is evidently based on the Poltergust 3000, being a vacuum cleaner kart. Mario Kart Arcade GP DX features a kart similar to this, though since it's green and simply called Vacuum Star, it loses any reference to Luigi's Mansion.
King Boo also appears as the mission 4 boss, but this is most likely just a reference to Super Mario 64 DS since all other bosses in Mario Kart DS are taken from that game.
Mario & Luigi: Partners in Time
November 28, 2005
Professor E. Gadd returns from Mario & Luigi: Superstar Saga, this time in a more major role, creating the Time Machine used by the main characters to travel back in time. In addition, when the Mario Bros. travel into the past, they meet the younger E. Gadd whose lab is destroyed by a volcanic eruption, and he says he will set up a new lab in Boo Woods, foreshadowing Luigi's Mansion.
Mario Basketball 3on3
July 27, 2006
The titular mansion from Luigi's Mansion appears as a playable court in the game. While playing ghosts will sometimes grab the ball.
Super Paper Mario
April 09, 2007
The "Mansion Patrol" minigame consists of shooting Boos in a mansion, and might be based on Luigi's Mansion.
Mario Party 8
May 29, 2007
The "King Boo's Haunted Hideaway" board is a haunted house-themed board featuring King Boo as the main attraction. King Boo also returns in Mario Party 9 as a boss.
Additionally in the "Specter Inspector" minigame the player has to explore a mansion in first persion view, using an electric lantern to search for three of eleven hidden enemies. This whole concept might be based on Luigi's Mansion, but ghosts from that game even appear sometimes, paralyzing the character for a short time.
Super Mario Galaxy
November 01, 2007
Luigi is first met in the "Ghostly Galaxy", a haunted-themed galaxy, being kidnapped by the ghost Bouldergeist and later saved by Mario. This might be a reference to Luigi's Mansion.
Mario Super Sluggers
June 19, 2008
A "Luigi's Mansion" stadium is unlockable in the game after buying Luigi's Flashlight in Pianta's Shop, and is only playable if the player has unlocked the night time settings. The playfield is actually in the mansion's backyard and features gravestones with ghosts that come out of them harming the characters if they get too close to them.
The "Ghost K" minigame takes place in the Luigi's Mansion stadium and consists in throwing balls at ghosts from Luigi's Mansion
Mario Sports Mix
November 25, 2010
The Luigi's Mansion court returns from Mario Basketball 3on3 as a basketball and volleyball court. It still features the ghosts grabbing the ball.
Additionally Luigi uses the Poltergust 3000 as one of his special attacks.
Luigi's Mansion: Dark Moon
Luigi's weapon in this game is called the Poltergust 5000 and is an upgrade of the Poltergust 3000. The fact that the number went directly from 3000 to 5000 might reference the Poltergust 4000 from Mario Kart DS.
Mario Party 10
March 12, 2015
The game features a Luigi Board, only available in amiibo Party mode by using the Wario amiibo. It's based on Luigi's Mansion: Dark Moon, featuring many elements from that game, such as Greenies, Boos, Gloomy Manor, King Boo, and a giant replica of the Poltergust 5000. The music for the board is also a remix of the Luigi's Mansion theme.
Super Mario Maker
September 10, 2015
One of the unlockable costumes that Mario can wear in the game by using a Mystery Mushroom is based on Luigi, and while he technically is just a Mario character, when worn the costume replaces the sound effects with sounds from Luigi's Mansion. It's unlocked in the 100 Mario Challenge mode or alternatively by using the Luigi amiibo from the Super Mario series, or the one from the Super Smash Bros. series. The costume is just a recoloring of Mario's sprite using Luigi's colors.
An update later also added a costume based on Professor E. Gadd from Luigi's Mansion.
Mini Mario & Friends: amiibo Challenge
January 28, 2016
Mini Luigi's levels in the game are based on Luigi's Mansion, including Mini Boos as enemies, and featuring the mansion theme as the background music.
This only counts as a type 2 link since the elements in the levels are all toys.
Copyrights for both series are held by Nintendo.