Yoshi no Tamago
Yoshi no Tamago (Yoshi's Egg), called Yoshi in America, is the first game in the Yoshi series and stars Yoshi, a character originally from Super Mario World. It was called Mario & Yoshi in Europe, thus being (arguably) part of both series.
The game is a simple puzzle game in which the player actually controls Mario and tries to destroy enemies from the Mario series: Goomba, Blooper, Boo and Piranha Plant. Players control Mario and Luigi in two players mode. These characters also return in later Yoshi games, with adult Mario appearing in Yoshi's Cookie and Yoshi's Safari.
Despite the start of his own series, Yoshi remains a central character in the Mario series, appearing in many other Mario games, most notably Super Mario Sunshine, New Super Mario Bros. Wii, Super Mario Galaxy 2 and every sport, party and racing Mario game.
July 14, 1993
A rail shooter game, the player actually controls Mario, shooting enemies while riding Yoshi, who walks on his own; for this reason the game is often considered part of the Mario series.
This game takes many characters from the Mario series, including Koopa Troopa, Lakitu, Peach and Bowser, that make appearences in later Yoshi games.
Super Mario World 2: Yoshi's Island
August 15, 1995
The first "Yoshi's Island" game, it's the first Yoshi platformer and the game that truly defined the Yoshi series. The game is called "Super Mario World 2" just because is the second main Mario game for the SNES, but the plot is actually a prequel to the Mario series. Mario himself only has a supporting role as Baby Mario, being carried around by the Yoshis, while the main villain is Baby Bowser and Baby Luigi is the "damsel in distress" character. For these reasons the game is often not even considered part of the Mario series, despite its title. So elements originating in this game are often (and also in this page) considered "Yoshi" elements, that create a link if they happen to appear in any Mario game (an example is Baby Mario, in Mario Golf 64 section).
Many elements from Mario games return here to become defenitley part of the Yoshi series, most notably the Shy Guys enemies from Super Mario 2 (USA). Is also notable that while this is the canon debut of Baby Mario, Baby Luigi and Baby Mario, baby versions of them already appeared in other media (such as Baby Koopa in The Super Mario Bros. Super Show! episode "Three Men and a Baby"), but looking very different, with Mario and Luigi even being mustached.
This game features Yoshi's ability to launch eggs and made it famous, but he actually already had this ability in Super Mario Kart.
Super Mario RPG: Legend of the Seven Stars
March 9, 1996
Yoshi's Cookies from Yoshi's Cookie appear as items in Super Mario RPG. They can be used in battle to summon Yoshi to eat an enemy and defeat it in one hit. However some enemies can't be eaten, so if a Cookie is used Yoshi will return it to the player or will give a Yoshi Candy item instead.
Yoshi's Cookies are also required to challenge Boshi into a race and can be used during it to boost Yoshi.
Mario Kart 64
December 14, 1996
Yoshi returns as a playable character, but this isn't a reference to the Yoshi series because he's also a Mario character and alredy was in Super Mario Kart. What it's worth noting is the new Yoshi-themed course, called Yoshi Valley. This is a unique course taking place over a big canyon with many twists and turns, offering the players different ways to end the race. Near the end of the course, there is a giant rotating Yoshi Egg that serves as an hazard.
However this stage's landscape and the giant Yoshi's Egg don't actually resemble any element from the Yoshi series, so this is simply a stage dedicated to it without any particular reference, but may actually be just a reference on Yoshi as a Mario character.
December 21, 1997
Stages 2-3 and 2-4 take place in the sewers and are designed as if they were made out of old newspapers. Some of the writings on them actually read "Mario" and "Luigi". Other writings include "Yoshi", "Nintendo", "N64", "Zelda" and "Pikachu".
Mario Golf 64
June 11, 1999
Baby Mario, the child version of Mario originally from Yoshi's Island appears here as a playable character. He appears a little older than his original appearance, and is redesigned to wear the same outfit as his adult counterpart, probably to let him play golf normally.
He also returns in Mario Golf GB, and becoming an effective Mario character he also appears in other later games. Specifically he appeared as a playable character in: Mario Tennis 64, Mario Tennis GB, Mario Kart: Double Dash!!, Mario Superstar Baseball, Mario & Luigi: Partners in Time, Mario Super Sluggers and Mario Kart Wii.
Mario Kart: Super Circuit
July 21, 2001
Apart from the recurring Yoshi racer, this game once again features a Yoshi-themed stage, called "Yoshi Desert", taking place on an Egypt-like desert with pyramids and a Yoshi Sphinx statue in the background. Because this place is totally original for this game, it's unknown if it's made to reference the Yoshi series or simply Yoshi as a character, but the second case seems more likely. The same Yoshi Sphinx returns in the Dry Dry Ruins course in Mario Kart Wii.
An effective reference to the Yoshi series is instead in the Shy Guy Beach course, that features a Pirate Guy ship from Yoshi's Story's level "Shy Guy's Ship", only slightly redesigned. This course returns as a "retro track" in Mario Kart Wii.
Yoshi's Island: Super Mario Advance 3
September 20, 2002
A remake of Yoshi's Island, it's still part of both series, but this time the "Mario" title has been downgraded to sub-title.
The game features some changes from the original, but no new references between the two series.
Mario Kart: Double Dash!!
November 7, 2003
Baby Luigi, the child version of Luigi originally from Yoshi's Island appears here as a playable character along with Baby Mario, who already appeared in other Mario games. Like Baby Mario, he's redesigned to look a little older and wear his adult counterpart's outfit.
Baby Luigi later returned as a playable character in each game also Baby Mario starred in: Mario Superstar Baseball, Mario & Luigi: Partners in Time, Mario Super Sluggers and Mario Kart Wii.
Yoshi's personal kart, the Turbo Yoshi is shaped like Yoshi's face, resembling his Yoshi Car transformation from Yoshi's Island. Also Birdo's kart, the Turbo Birdo is a "Birdo" version of it.
Also, the Battle Course "Cookie Land" is based on Yoshi's Cookie and takes place on a giant Cookie. Cookies shaped like Yoshi's face can also be seen in the background. This course returns as a "retro track" in Mario Kart Wii.
The game features another Yoshi-themed course: Yoshi Cirscuit, taking place on a Yoshi-shaped island. However, considering that most of the game's courses are character-based (e.g. Luigi Circuit, Peach Beach, Daisy Cruiser, Waluigi Stadium, etc.), this probably just references Yoshi as a kart racer, rather than referencing the Yoshi series.
Super Mario 64 DS
November 21, 2004
This remake of Sumer Mario 64 features Luigi, Wario and Yoshi as the new selectable characters, but Yoshi is the one with the most important role, being the new starting character, with the other three unlockable. His gameplay is taken from Yoshi's Island with only some differences. His special ability after getting a Power Flower is the Fire Breath, like his move from Super Mario World and Yoshi's Island. Yoshi is also unique in the fact that he has no cap for the other characters to wear, while he can freely wear theirs to shape-shift into them.
Another reference is in the "Love Me...?" Minigame, that features a flower identical to the one in Yoshi's Story's "Smile Meter". This minigame is also featured in New Super Mario Bros.
Mario Superstar Baseball
July 21, 2005
The game features a Yoshi-themed stage, called "Yoshi Park", that's entirely made of cardboard, referencing Yoshi's Story.
Mario & Luigi: Partners in Time
November 28, 2005
In this sequel to Mario & Luigi: Superstar Saga, Mario and Luigi travel back in time to meet their younger selves. However, while Baby Mario and Baby Luigi already appeared in previous Mario games, this game also includes Baby Bowser, previously only featured in Yoshi's Island and other Yoshi games.
The game also canonically introduces Baby Peach, the young version of Peach (though a baby version of the princess already appeared in The Super Mario Bros. Super Show! episode "Three Men and a Baby".
Yoshi's Island DS
November 13, 2006
In this sequel to Yoshi's Island, Baby Mario, Baby Luigi and Baby Bowser return from the previous game, but there also is Baby Peach, the character originally from Mario & Luigi: Partners in Time. Each baby has a special ability, and Peach's to float, just like she did in her previous playable appearances in Super Mario Bros. 2 and Super Paper Mario. Her parasol's design also seem to be based on Super Paper Mario.
Other babies introduced in this game are Baby DK, child version of Donkey Kong, Baby Wario, child version of Wario, and in the ending cutscene Baby Yoshi (though generic Baby Yoshis already appeared in the Mario series). Baby Link (Zelda series) and Baby Olimar (Pikmin series) also make cameos.
Mario Super Sluggers
June 19, 2008
This Babseball game features various baby characters, including Baby DK, originally from Yoshi's Island DS.
Other babies featured are Baby Mario, Baby Luigi, Baby Peach and the debuting Baby Daisy.
Mario & Sonic at the London 2012 Olympic Games
October 13, 2009
The stage for the Dream Long Jump even is "Yoshi Picture Book" and takes place in the Rail Rift stage from Yoshi's Story.
Mario Golf: World Tour
May 1, 2014
The game features a court called Yoshi Lake, which is based on Yoshi's Story and Yoshi's Woolly World. The music is a remix of music from Yoshi's Story.
Yoshi's Woolly World
June 25, 2015
The Bullet Bill Patch, a bidimensional variant of Bullet Bill, is designed after the Bullet Bill sprite from Super Mario Bros.
Likewise, the Monty Mole Patch looks similar to the Monty Mole sprite from Super Mario World, although it doesn't look exactly the same.
Yoshi's Woolly World also features compatibility with many amiibo, and scanning a supported one unlocks a pattern for Yarn Yoshi based on the respective character.
All amiibo from the Super Mario series released at the time are supported, and while most of them were also released in the Super Smash Bros. line and unlock the same costume, Toad is exclusive to the Super Mario line.
The unlocked patterns are:
The Donkey Kong, Rosalina, Wario and Diddy Kong amiibo released later in the Super Mario series unlock the same patterns as their Super Smash Bros. counterparts. (see here)
Super Mario Maker
September 10, 2015
Five of the unlockable costumes that Mario can wear in the game by using a Mystery Mushroom are based on different versions of Yoshi, specifically one is based on regular Yoshi, and when worn it replaces the sound effects with sounds from Yoshi's Island.
The other four costumes are based on different forms of Yoshi from Yoshi's Woolly World, specifically: Woolly Yoshi (Green Yoshi), Pink Yarn Yoshi, Light-Blue Yarn Yoshi and Mega Yarn Yoshi; when worn they replace the sound effects with sounds from Yoshi's Woolly World.
Regular Yoshi can alternatively be unlocked by using the respective amiibo from the Super Smash Bros. series or the Super Mario series, while each of the four Yarn Yoshi can be unlocked by using the respective amiibo from the Yoshi's Woolly World series.
Mini Mario & Friends: amiibo Challenge
January 28, 2016
Mini Yoshi's levels in the game are based on Yoshi's Woolly World, but also feature the main overworld theme from Yoshi's Island as the background music.
This only counts as a type 2 link since the elements in the levels are all toys.
Poochy & Yoshi's Woolly World
January 19, 2017
The 3DS version of Yoshi's Woolly World includes the same amiibo feature as the Wii U version, including all the same patterns, but also adding ones based on more recent amiibo.
This includes all the Super Mario amiibo released at the time, though since Donkey Kong, Rosalina and Diddy Kong simply unlock the same patterns as their Super Smash Bros. counterpart, their compatibility is considered incidental.
New patterns exclusive to Super Mario amiibo are:
Super Mario Odyssey
October 27, 2017
This game features compatibility with many different amiibo, that when scanned will be recognized by Uncle amiibo. This includes all Yoshi series amiibo; the Yarn Yoshi amiibo will be called "Yarn Yoshi" in any of its variations, while the Poochy amiibo will be called Yarn Poochy.
This creates a sub-universe link with the Yoshi series because Uncle amiibo says the character's name out loud within Mario's universe, it's not just an on-screen message.
Copyrights for both series are held by Nintendo.