Super Mario Bros.
Console gaming would not exist if not for Super Mario Bros.
I know what you must be thinking. Consoles existed years before Super Mario Bros. Even the Famicom somehow managed to get along for around two years without it. All of this is true enough. But bear in mind that back in those earlier years, most console best-sellers were just home ports of arcade games. Now you may be thinking, Super Mario Bros. was itself actually in arcades, so maybe it would be best to begin by properly defining the distinction we're working with here.
Back when arcades were the primary vector for games, those games had a certain simplicity to them. You had a single static screen, there was a character on it, there were a bunch of things trying to kill that character, and there was some stuff to collect, or destroy, or whatever. The player did whatever they game tasked them to do, at which point everything would reset with the speed cranked up, and maybe a harder variation of the enemies tossed in here and there. That was pretty much it. You just repeated the same activity over and over, the action becoming faster and harder each time, until eventually you couldn't keep up and ran out of lives. The only real goal was simply to do better than you'd done last time, or to score higher than your peers. The closest thing to the modern notion of finishing a game was to become some sort of madly driven savant, staying alive and running through the iterations until some variable involved in the endless difficulty increases exceeded trackable size and bugged the whole game out—something few ever considered a real goal.
There were some relatively ambitious variations to this concept before Super Mario Bros. came along, the most famous being its predecessor Donkey Kong, which cycled through a series of four different screens before looping over with increased difficulty. Moon Patrol and Paper Boy had relatively long scrolling levels. Cloak & Dagger even featured an honest to goodness progression of 33 unique levels. Yet all of these games were still firmly rooted in the arcade philosophy. In Moon Patrol, you shoot when you see an enemy, jump when a pit approaches, and repeat. In Cloak & Dagger, more and more deadly things clutter it up, but you're still just flitting back and forth across a single static screen, setting off the bomb in the middle for extra points.
Then along came Super Mario Bros. to deliver what was truly an epic, industry-changing experience. It wasn't just a question of having 32 scrolling levels before the loop. Gauntlet could make a similar boast the same year, but it was definitely designed as an arcade game: An endurance test. If anyone else at the time had designed Super Mario Bros., the first level would simply have been a long open stretch with two pits, a few enemies, and a fairly generous scattering of coins. Then you'd run across what was essentially that same open plain, with more enemies and more pits, with nothing really changing except for a new enemy type appearing every four levels until eventually the game forced you to keep running past 30 Hammer Bros. with the speed cranked higher each time.
Instead, Super Mario Bros. decided to present something more like a narrative. Here's Mario in this happy valley. A little mushroom wanders over. Clearly it's an enemy, so Mario jumps over it. A shiny brick looms overhead, so he jumps, and another mushroom appears, rushing towards him! He can't escape, it hits him and... he grows? Suddenly he can smash through the scenery! He can crush his enemies underfoot! Fearless and confident, he bounds along, eventually reaching a small structure. After a quick rest within, he finds a huge pipe, granting him access to a strange subterranean cave. It's a little creepy down here, with man-eating plants in the pipes, but eventually he reaches the surface again. Cutting across some hilly terrain, he finds a huge castle full of lava and whirling flames! Eventually he reaches a long bridge, guarded by a fire-breathing dragon! Barely squeezing by, he grabs an axe and cuts the bridge supports, dropping the huge monster into the lava below, and rescuing... a strange little mushroom man, explaining that the princess he seeks is in another castle. Finding another pipe out back, he finds himself underwater, swimming past currents and huge squids!
The experience is constantly changing. Here's a level with platforms on pullies, one lifting as the other falls under Mario's weight. Here's a long bridge with fish leaping out of the water. Here's a land of giant mushrooms, requiring a running start to make the huge leaps from cap to cap. Here's a castle which seems to loop endlessly until you figure out the correct sequence of pathways to break its weird magic and reach the end. While experience with the basic controls and enemy types always comes in handy, each new level is a unique experience, with new skills to learn in order to proceed. Then there's those extra touches where different sorts of areas having different music, and goombas being grey instead of red when not out in the daylight.
Impressive as all this is, it's actually quite horrible as an arcade game. The player puts their quarter in, and buys a handful of lives. Each new lesson the game has to impart is likely going to cost one or two. Now, in something like Joust, odds are you won't make much progress on your first few quarters, but once you get a feel for how the birds handle, you're going to start getting a lot of mileage. Odds are you won't be consistently dying until pterodactyls start to be tossed into the mix.
Not so with Super Mario Bros. Once you have a handle on the basic jumping physics, you'll likely die to the first piranha plant. Once you understand those, you'll be dying from accidentally kicked shells. Then from Bowser's fire breath. The unpredictable movement of bloopers. Every new level has a new way to die, and a few deaths mean starting over from scratch! People weren't willing to put up with that in Dragon's Lair, and that even had the appeal of getting to watch a Don Bluth movie if you stuck it out.
On the other hand, this made the NES version a great buy. Being able to start over any time you wanted, and not having a line of other players at your back, you could eventually figure the whole thing out, play it through, and finally find that one castle the princess was actually in. Once you finally did that, sure, you could loop back through to the very beginning, play everything over again with buzzy beetles replacing all the goombas, but it didn't feel necessary. Seeing the journey through to the end was accomplishment enough that getting the highest score possible seemed rather trivial in comparison.
Then, of course, there were all the little secrets. Some pipes could be entered by ducking on them, leading to little coin-filled rooms. Jumping in just the right spot would reveal hidden bricks with coins or even 1UPs. Finishing a level with the timer in just the right spot netted you a fireworks display. Then came that greatest of discoveries: Climbing up onto the roof in World 1-2 let you bypass the pipe leading back to the surface and discover the first warp zone. This isn't even getting into those "secrets"—intentional or otherwise—like what happened when you hit Bowser with eight fireballs in different castles, or how racking up enough 1UPs by trapping a koopa shell against a wall would spill the general graphics into those for counting lives, yielding totals like "part of a flag 5" after enough bounces.
The legacy of Super Mario Bros. was a sudden shift from arcade quarter-munchers to elaborate platformers. Eventually score counters would be dropped entirely, and games lasting several hours would allow for play across multiple sessions through passwords and battery-backed save files. Lining up at the arcade to compete against people in the latest quarter-muncher lost its appeal when one could set down with the rich experience that was Mega Man 2 or the unparalleled joys of Super Mario Bros. 3. Once people started to realize this, a fundamental shift took place in the minds of designers all over. While this sort of length and sophistication may have come about without Mario leading the way, Super Mario Bros. was the game that planted the flag for the empire of Depth in the untamed wilds of the home console market.
Oh, and let's not forget the impact Super Mario Bros. is still having on game designers to this day, with full recreations of that astoundingly memorable first level finding their way into modern games from New Super Mario Bros. to Super Smash Bros. Brawl, and serving as the clear starting point for quirky indie games like Braid and Eversion. Really, Super Mario Bros. isn't so much a classic as it is the classic.