Sonic X-Treme was a Platformer game planned for the Sega Saturn. It was meant to be Sonic the Hedgehog's official jump to 3D, however the game was cancelled after an enormous amount of development troubles.
With the release of Super Mario 64, the world was properly introduced to 3D platformer games. Following it many existing franchises did the jump from 2D to 3D, many of which didn't go well such as Bubsy with Bubsy 3D. Likewise many new mascots joined the Platformer genre with 3D games, such as Crash Bandicoot. So naturally Sega fans were eagerly expecting Sonic the Hedgehog to do the jump to 3D as well, however...
Sonic 3D Blast was released to be Sonic's first 3D game, but the game used isometric view which merely gives the illusion of 3D and it was very poorly recieved. Sega decided to make a real Sonic 3D game, originally the game was being developed for the Sega 32X add-on, but due to terrible sales and the Sega Saturn being released, they moved the game to the Saturn. Yuji Naka clearly showed little faith in the project, as when he was shown a prototype all he said was "Good Luck".
At first the development of the game seemed to be going well, a reveal trailer was shown promising Sonic's jump to 3D. However the developers overestimated the Saturn's capabilities, as when they attempted to run the game in an actual Saturn it simply wouldn't work. This was because the Saturn was built for 2D rather than 3D. Sega of Japan was infuriated by the lack of progress they had done.
Sega attempted to give the team the game engine from Nights Into Dreams to use as starting point to get the game working to run in a Saturn, but when Yuji Naka found out he threatened to quit unless they stopped. The team was split into several smaller teams to build new engines. This predictably only caused more problems, comunication between the teams was minimal and the deadline for release was coming soon.
Developers worked for hour and hours non-stop for months. Eventually the enormous amount of stress caused the lead developers to become ill and were told by doctors that they would die in 6 months unless they retired from the project immediately. At this point, Sega gave up and officially cancelled the game.
With the game cancelled, the Sega Saturn was left without a geniune Sonic the Hedgehog game. Sonic 3D Blast was hastily ported to the Saturn and Sonic R was also released, but neither were a true jump to 3D nor an authentic platformer Sonic game. The game's cancellation is frequently considered to be one of the main factors to the Sega Saturn's demise, which was already struggling before the game was even announced.
With Sonic lacking a 3D platformer, many other 3D platformers including Mario quickly gained popularity with little competition from Sega, which also contributed to Sega's declining reputation. Sonic went through a long drought, almost skipping an entire console generation.
Sonic's jump to 3D was delayed until the release of Sonic Adventure. Some concepts from X-Treme were later used in Sonic Lost World
Many argue about how Sonic X-treme would've impacted the game market, and wether or not it could've saved the Sega Saturn.