Note: If you haven't played all the Yoshi games there may be some spoilers on this page! Read at your own risk.
Yoshi is a bipedal green dinosaur who wears shoes and a saddle, though the latter doesn't get much use any more. The fact that Yoshi has been steadily standing straighter over the years as Mario rides him less may or may not be a coincidence...
Yoshi, to the best of my knowledge, first appeared on his namesake NES game, which was also released as a Gameboy game. It was a fairly simple puzzle game that involved matching up enemies falling down a screen or sandwiching them between egg shell halves.
His first real appearance was in Super Mario World for the SNES, along with Mario, where the mustachioed plumber rode him throughout the Mushroom Kingdom as he vanquished the koopalings and rescued Yoshi's friends from their castles. There were the first four different colours of Yoshies, but the green one has always been the official one. It seemed that Yoshi could speak english here, though he couldn't do most of his trademark moves that he can today, like the flutter jump and enemy swallowing.
Yoshi then had three games for the SNES released with his name on them; Yoshi's Cookie, Yoshi's Safari, and the most famous one, Super Mario World 2: Yoshi's Island, more commonly referred to as just Yoshi's Island. Yoshi's Cookie was another puzzle game, though with a fairly new style of game play, involving lining up cookies to make an entire row or column of the same type. A special note though is that there was a separate release for Japan which included actual recipes and in-game mini-games for making three different Yoshi cookies - heart cookies, flower cookies, and battenburg cookies - which you could do at home. Sadly this was omitted from the English release (can't imagine why). Luckily through the power of Emulation and my abilities to bumble about with a Japanese dictionary, you can read full translations of all the recipes here!
Yoshi's Safari was a Super Scope game where you played as Mario riding on Yoshi's back beating up the koopalings and thwarting another evil plan of Bowser's. The Super Scope infamously gorged itself on batteries, so I would recommend that you emulate the game if you want to play it.
Yoshi's Island, one of the greatest 2-D platformers ever created, was also recently re-released as Super Mario Advance 3, with added levels and some new features, like the addition of sound effects from Yoshi's Story. Yoshi's Island takes place back when Mario was a baby, and tells the story of how they first came to meet each other and become friends. This is the more widely accepted theory, as opposed to the one from the cartoon series, where Luigi found Yoshi's egg and adopted him. Yoshi carried baby Mario to his brother baby Luigi at baby Bowser's castle, thus saving them from the clutches of the magikoopa Kamek.
Yoshi and the characters from Yoshi's Island also appeared in Tetris Attack, an addictive SNES puzzle game which was later released on the N64 as Pokemon Puzzle League, exploiting the pokemon craze present at the time. Tetris Attack, however, was converted from the Japanese SNES release of the same game, which starred original characters and was called Panel De Pon. The title screen of the American release (Tetris Attack) featured Yoshi song, which has only been present in Yoshi's Story and this game.
Yoshi also appeared in many other games, like Mario Kart, but not as a main character. His next big appearance was technically on the N64 where six newly hatched Yoshies set out to break baby Bowser's spell which had turned Yoshi's Island into a giant storybook. The voices recorded for this game have been recycled for almost all subsequent games where Yoshi has a part, since he supposedly cannot speak english. Another notable thing from this game was the sounds of Yoshies singing that could be heard in the game - this, however, tended to annoy more people than it pleased. Yoshi song has never been heard in any game since, which is a pity, since it doesn't sound too bad with the volume turned down a few notches.
On the Gamecube, Yoshi has only played side parts in games like Mario Kart: Double Dash!!, and had a side role in Super Mario Sunshine, but has yet to appear in a game of his own for Nintendo's next-generation console. Hopefully, it's only a matter of time until he makes his way onto a minidisc for the Gamecube. Failing that, we can only hope he gets a fully-fledged game of his own for the Wii.
Since there's confirmation in a few games that Yoshi isn't the only one of his species, and that other Yoshies are simply different colours, a lot of people use Yoshi recolours* as their avatars *, but some people 'customise' their Yoshi with clothes, wings, eyebrows, and so on.
A debate among the Nintendo fanbase is whether or not there is anything
between Yoshi and a very similarly modelled creature called Birdo, who
first appeared in Super Mario Land 2, that one in Subcon where you had to
fight the Birdos at the end of every stage. If you compare the 3-D models
from Mario Kart: Double Dash!!, then you'll see any number of similarities,
but the main difference is the head and, probably significantly, their
gender. Although a few crosses of Yoshi and Birdo have been thought up on
the net, in the games they simply remain friends since they've only
appeared together in Mario Tennis and MK:DD.
Even though, if you look closely, since she came onto the Gamecube Birdo has been wearing a FREAKING HUGE DIAMOND RING that I somehow managed not to notice for the longest time.
Yoshi is a far more popular character in Japan where they tend to go for cuteness more than America does, but as you can see by doing relevant Google searches, there are still many people in the western world who could be considered his fans. Some of them, like myself, put a lot of work into what they do for their sites, usually as a hobby more than anything else.
MISSING: Description for Yoshi's Universal Gravitation.
MISSING: Description for Yoshi's Touch & Go.
MISSING: Description for Mario Kart DS.
The Yoshies also had a cameo appearance in Mario & Luigi: Partners in Time. In the past you had to travel to Yoshi's Island in pursuit of Baby Bowser, and stumbled across a seemingly abandoned Yoshi village. It soon transpires that a horrific, gigantic creature (external link) bearing a moderate resemblance to Kara Yoshi (external link) has been terrorizing the island, and it's up to the Mario brothers and their younger selves to stop it and save the Yoshies!
In Yoshi's Island DS, you again take control over Yoshi and help not just baby Mario, but baby Peach, Donkey Kong, Wario, and even Baby Bowser! It seems that the present-time Bowser has travelled back in time (the Mario universe characters have no respect for the space-time continuum) to capture all the babies in the hope of finding the special star children. Each baby has different abilities and you must guide Yoshi and the babies, along with the helpful stork, across Yoshi's Island to confront bowser in his floating castle and rescue all of the mushroom kingdom's children! It didn't make any use of the DS's touch screen, but the screen was split across both and you could choose to have Yoshi on the top or bottom in order to see further above or below you. The graphics were given a revamp, but apparently Artoon (who got rights of use in order to make the game) gave an underpaid intern part of the work because the musical score for the game is extremely lacking. It's not bad, just very dull and unimaginative.
Yoshi has also appeared in every installment of the Super Smash Brothers series as a non-hidden character, yet despite being in every game, he's the only character from the Yoshi games series to ever show up in the games! The best he gets is his own special stages.