Mario himself is named after Mario Segale, an American warehouse landlord who worked with Nintendo in the 1970s and 1980s, and whom the character happened to resemble.
The two bullet enemies are named Bullet Bill and Torpedo Ted, which would make them a possible reference to Bill & Ted by the American localisers (the same enemies are called "Killer" and "Torpedo" in Japan).
The Star Bits from Super Mario Galaxy are based on a star-shaped candy called konpeitō which is popular in Japan.
In the German version of Yoshi's Island, Naval Piranha is called Audrey, a reference to Audrey Junior from The Little Shop of Horrors. The Piranha Plants in the series were also based on Audrey Junior.
Burts dress like Obelix. Probably a coincidence, but the French and German translators noticed it and gave them names which are anagrams of "Obelix" (Bélixo in French and Elixbo in German).
In the German version of Paper Mario: The Thousand-Year Door, Fahr Outpost is called Großfrostheim, which means "Great Frost Home". This however is a reference to the German city Großostheim, which is where the Nintendo of Europe headquarters are located, and where the game was localised.
In Paper Mario 64, Luigi keeps his diary in a secret basement under his and Mario's house. If you manage to read the entries, you can find one entry reveals Luigi is afraid of ghosts, and another where he says he wants to have the lead role in his own adventure. These diary entries are referencing Luigi's Mansion, which was in development at the time.
Mario Kart 64 originally contained several nods to real world products such as Marlboro cigarettes, Agip gasoline, Mobil 1 oil and Goodyear. They were altered internationally for two likely reasons; one of the companies parodied sold cigarettes (possible trouble for an E rated game) and any of them could have sued. The names Marioro, Luigip, Yoshi 1 and Koopa Air were changed to Mario Star, Luigi's, Yoshi and Koopa Air (the Koopa Air logo was changed to make it less similar to the Goodyear logo).
Shigeru Miyamoto had originally intended for Bowser to be an ox, and based him on the main antagonist from the animation Alakazam the Great (Saiyu-ki in Japan), King Gruesome/Gyu-Mao. This is likely why his modern design has horns and a defined muzzle, despite him being a turtle.
The Koopalings were based on seven of the Super Mario Bros. 3 developers. They were all later named after musicians by the American localisation team, as no distinct names were given in the Japanese version. (Larry Koopa - Larry Mullen, Jr., drummer for U2. Morton Koopa Jr. - Morton Downey, Jr., singer and host of The Morton Downey Jr. Show. Wendy O. Koopa - Wendy O. Williams, lead singer of Plasmatics. Iggy Koopa - Iggy Pop, lead singer of The Stooges. Roy Koopa - Roy Orbison. Lemmy Koopa - Lemmy Kilmister, lead singer and bass guitarist of Motörhead. Ludwig von Koopa - Ludwig van Beethoven.) It's also speculated the musical names were chosen because their scepters resemble microphones.
The seemingly random symbol on the mail box of Yoshi's house in Super Mario World is actually the Yūbin mark, the service mark of Nippon Yūsei Kōsha (Japan Post).
An issue of Nintendo Power revealed that Shigeru Miyamoto got the idea for Boos from the wife of his co-worker and close friend Takashi Tezuka, as she is shy but one day got very angry at him for coming home late from work. Boos were also originally named "Boo Diddleys" after the late Blues singer and guitarist Bo Diddley.
The "The Manta Storm" mission in Super Mario Sunshine seems to be referencing The Shining. At the end of the book, one character notices, "a ghostly manta shape, floating away over the hotel. It was paper thin, like a shadow, and then broke into smaller forms before turning into smoke and drifting away." You complete the mission by spraying the paper thin manta, making it break up into smaller and smaller pieces until they vanish in a puff of smoke.
The Super Mushrooms are based on a fungus named Amanita muscaria, commonly known as the fly agaric or fly amanita. They make the user feel as though they are growing in size. This effect was also referenced in Alice's Adventures in Wonderland, which could be where Shigeru Miyamoto got the idea from.
An island in Super Mario Bros. 3 looks like Japan, and its castle is where Kyōto would be, Nintendo headquarters. The king of this castle looks like Mario, who you could say is the king of Nintendo.
The Warp Whistles are the Recorder from The Legend of Zelda I. Your character will play the same melody on them, then a whirlwind will take him away.
In Mario Golf: Toadstool Tour, whenever the player hits a golf ball into a patch of flowers outside the Peach's Castle level, Pikmin will come flying out, crying in pain.
The Chain Chomp enemies were inspired by a dog, chained to a post that belonged to a neighbour of Miyamoto during his childhood.
Both Link and Samus make guest appearances in Super Mario RPG. Speaking to Samus will make her say "I'm resting up for Mother Brain" and speaking to Link will trigger the puzzle solved jingle commonly heard in The Legend of Zelda games.
The Goomba enemies' design is based on shiitake, though oddly the enemies are named "Kuribō" in Japanese, which roughly translates as "chestnut people", possibly due to someone mislabelling their model thinking that they resembled chestnuts. This could also be why the Goombas in Super Mario World resemble chestnuts, but those aren't really Goombas, as they're defined as a separate enemy called "Kuribon" in Japanese and "Galoomba" elsewhere.
Bowser's Japanese name, Koopa, comes from a Korean dish called "gukbap", which is known in Japanese as kuppa (a Japanese approximation of the Korean word). Other dishes Bowser was almost named after are Yukke (from the Korean yukhoe) and Bibinba (from the Korean bibimbap). Though the Koopa Troopa enemies inherited Bowser's Japanese name, they were actually named "Nokonoko" in Japanese, which is a Japanese onomatopoeia word for doing something nonchalantly or unconcernedly.