Graphics are everything in the world of videogames - the capabilities of a graphics engine can completely change everything about what a game will ultimately be. The greater graphical abilities of the Playstation is what brought Square and Final Fantasy to Sony, the Mode 7 capabilities of the Super Nintendo allowed F-Zero and Super Mario Kart to exist at all, and the chunky graphics of the N64 captured James Bond's weird square hands for the first time ever.
But sometimes graphics can seemingly hold stuff back too. After all, each generation of videogames has their limits, and the developers are stuck working within those limits. But sometimes those limits can help define a character perfectly, in a way that more advanced graphics would have messed up. These are a few of those.
1. Crash Bandicoot looks the way he does because they didn't have any more polygons to flesh him out.
You only need to take one look at Crash Bandicoot to know why the wumpa fruit loving marsupial was a huge hit with fans from the start. His goofy grin, ungainly gait and big dumb shoes all combine into an instantly endearing character you can't help but want to go on an adventure/twirling backhand island natives with.
However, almost everything that makes Crash, well, Crash, is the result of the creators of the game simply not having enough polygons to work with. For starters, Crash's face was intentionally made as large and goofy as possible so that we could actually see it, this resulted in the character being designed with no neck, which resulted in his signature way of moving and turning to the camera. Speaking of movement, Crash's shoes are a result of the poor resolution of the screen making it difficult to make out his limbs when he was moving. Hell, the only reason that Crash Bandicoot is orange is because that was literally the only color that didn't make him look like shit in contrast to the stages he appeared on. It's also the reason no stages containing lava appear in the original game.
So maybe "graphics got too good" is the reason we haven't seen a new Crash game in so long. Yeah, that's probably it.
Source: All Things Andy Gavin
2. Samus Aran's Power Suit was redesigned for a black and white game
Even though Samus invariably loses it at the start of every game she appears in, her Varia suit is still the most recognisable and unchanging element of the character. Weirdly though, it was never supposed to look the way it does now, in fact, in the original Metroid game collecting the Varia suit just used to turn Samus' currently equipped suit a bitchin' shade of pink.
As fabulous as that was, it wasn't an option for the second game, aptly titled Metroid II: The Return of Samus, because the console it was being developed for, the original Game Boy, only displayed in black and white. So, in order to show that Samus had obtained the varia suit without using color, her suit was redesigned to include shoulders that could level an entire city block. I'm guessing that the look struck a chord with someone because Samus has been rocking that look for at least the last decade.
Source: Metroid Database
3. Mario's look is based entirely on a lack of pixels
Characters don't come any more iconic than Mario, they also don't come any more ingenious. You see, almost everything about Mario's design, from his hat and moustache right down to his freaking profession is a direct result of Shigeru Miyamoto having only a handful of pixels to play with while designing the character.
Giving Mario a moustache meant that Miyamoto didn't need to give Mario a mouth, his signature hat meant that they didn't need to animate hair and his overalls allowed them to show where his arms were without too much effort. The end result was a short, squat, but more importantly sort-of-humanoid looking character that didn't take hundreds of pixels to animate and approximately billions of future dollars for Nintendo.