Games today may seem miles away from those of the 16-bit era in the early nineties, but when broken down to their basic elements, the common ground is easily apparent. With a far superior processor than its father, the NES, the Super Nintendo had the capacity to usher in new innovations. Most came directly from the Big N's own game makers, but all have been pioneers who've upgraded the pedigree of current developers smart enough to embrace their progeny.
Mario Paint was released back in 1992 and came packed with a mouse peripheral, which allowed gamers to draw and play many cursor-based minigames. There were actually quite a few games afterward that incorporated the device, and Mario Paint eventually became the inspiration for WarioWare and Earthbound. As for the rest of gaming, you may think of a mouse as a useless device for consoles, but today we see a fairly similar cursor-based control style with the Wii, PlayStation Move, and Kinect.
The amount of Street Fighter versions that have been developed is staggering. With so many sub-series for each numerical version, its boggling nowadays to think they all used to make it to retail shelves. Especially when mods and DLC will easily do the trick today. These things were non-existent back in the nineties, though, so any updates required a new cartridge. Of all the versions, Street Fighter II: Turbo brought the biggest influence to future fighting games: speed. Controller skills and finesse are easily mastered by today's audience, and just about all current fighting games require that ninja-level skill for a gamer to be labeled victor. So remember, young grasshoppers, you have Street Fighter II: Turbo to thank for sonic-speed fighting games.
Square Enix (Squaresoft at the time) has always succeeded in delivering a deep story with their role-playing entries, though the usual suspects have almost always used turn-based combat systems. Secret of Mana built the bridge between traditional RPGs and quicker, action-based combat. Also, the weapon flexibility and ability to strengthen power through use—basically leveling up the weapon—was a relatively new concept, but much lauded. The crown jewel of the Super Nintendo, Chrono Trigger, takes much away from Secret of Mana, as do many modern action/RPGs.
Before Super Mario Kart hit the scene, F-Zero, a launch title for the Super NES, paved the way for all future racing games, revitalizing the genre and even creating a sub-genre in futuristic racers. That sub-genre is sustained even today, as WipEout 2048—the newest game in a series heavily influenced by F-Zero—is a launch title for the PS Vita. F-Zero developers used graphics rendering, called "Mode 7," which created pseudo-3D effects onscreen, giving the environments much more realism. This sparked the imagination of programmers, and even more realistic racing series like Daytona USA credit F-Zero as an instrumental catalyst to the evolution of racing games.
A Link to the Past's biggest influence was probably in its own series. While the game was one of the most gorgeous Super NES titles, the basic gameplay conventions were quite similar to the first game on the original NES. However, it perfected the equipment which has been a staple of almost every game since, and its storyline revolving around a light and dark Hyrule has seen many permutations from Ocarina of Time to Twilight Princess. The backpack and menu interfaces were also something very polished for a game of the time, and its simplicity is what many overworked games today could learn a thing or two from.