Super Mario World (SNES, 1991)

Super Mario World (1991) was the game that was packaged with the brand new Super Nintendo Entertainment System.  The system was the direct response to Sega's "Genesis does" ad campaign, being Nintendo's first 16-bit system.  The new console could handle more color, sound, and action than the original NES, and arguably even more than the Genesis.  One clear advantage the SNES had over the Genesis was sound.  It had twelve channels of orchestrated sound that were used over its five year lifespan to craft some of the finest video game soundtracks in history.  Another revolutionary piece of technology the SNES had was Mode-7, which allows sprites to be re-sized, tilted and turned in three dimensions, giving games like F-Zero and Pilotwings a pseudo-3D look.
That said, Super Mario World is really Nintendo putting their best foot forward on the SNES's launch.  The game shows off all of the system's new capabilities while also perfecting the Mario formula.  The game is quite easily the best of all the 2D Mario platformers.  All of the innovations that Super Mario Bros. 3 introduced are fully realized in this game.  Where SMB3's eight world had separate map screens, the whole of SMW takes place on one congruent map, with twists and turns at every place imaginable.  Most levels have a normal exit and a secret one (or more), which branches each path off to give the game a completely non-linear style.  This is also the first Mario game to feature a battery for save files.
The story this time goes that Mario, Luigi, and the Princess are on vacation on dinosaur island, when who should kidnap her but the infamous Bowser.  The Mario Bros. are yet again tasked with saving her.  While travelling the first small bit of the island, they discover an egg that hatches before them to reveal a green dinosaur named Yoshi (who would become one of the series' most beloved characters).  Yoshi tells them that Bowser trapped him and his friends inside of eggs, and agrees to go along with them.
The Yoshis are one of the biggest additions to the game, and offer whole new dimensions to the platforming. Mario can ride on a Yoshi, whose main ability is eating enemies with their long tongues.  Most enemies are simply swallowed, but the koopas (who now come in four colors) give different effects.  Green koopas can be spat out as a sliding projectile at enemies.  Red koopas can be spat back out as fireballs.  Blue koopas give Yoshi wings, allowing him to fly temporarily, and yellow koopas  allow him to stomp on the ground and knock out nearby foes.  Yoshi can also jump on any enemy and walk on some surfaces that Mario cannot.  Some of the game's levels and secrets require the clever use of Yoshis to solve them.  If Yoshi gets hit, Mairo will fall off of him and the startled dino will rush back and forth until Mario jumps back onto him, or he stumbles off of a cliff.
The raccoon suit from the last game has been replaced with the cape, which works somewhat similar.  When Mario has the cape, he can fly by getting a running start, and then he soars into the sky, and tilting back on the D-pad at the right time will give Mario more height.  This takes a short while to get used to, but once you do, it can be used greatly to your advantage.  Unlike the raccoon suit, it won't run out if you are good at it, but can only go one direction at a time.  The fire flower returns, of course, but Super Mario World does not have as many power ups as SMB3 in favor of the excellent Yoshi system.
Nintendo had once again proven why Mario is their strongest intellectual property, and gave the SNES the killer application it needed to become the number one console for the next five years (until the Sony Playstation came out).  The Mario series is always raising the standards for the games that come out after it, and even still hold up against the modern games.  This is the last time Mario would have a 2D outing on a Nintendo home console (not counting Yoshi's Island), until New Super Mario Bros. Wii, and is the finest of all of them.  Mario would make a few deviations on the SNES and Game Boy (all excellent, regardless) but his next main series game would once again change the face of gaming.