The idea is older still: it looks like it came to D&D via Dave Arneson's Blackmoor
The dragon, a large mythological beast, is found in a variety of story telling traditions from multiple cultures. Some breath fire ("Smaug the Golden" being an example), some are just big and nasty (St George and the Dragon), some breath poison, and some are mystical beings who can shape change into human form. (Chinese myths and legends). Tolkien referred to a cold drake being killed by one of the ancestors of the Rohirrim (LoTR), and Ancalagon the Black being the greatest of flying dragons(Silmarillion, First age). In most stories, one dragon is villain enough.
As I touched on in this answer, dragons ended up in D&D as an eclectic mix of creatures inspired by a multiple story telling traditions. Putting multiple kinds and colors of dragon into one setting wasn't original to D&D, insofar as a story idea. The novel Dragonflight, published in 1968, was the first of the Pern dragon novels by Anne McCaffrey. She had multiple hues of dragons flying about, interacting with dragon riders and other characters while battling the Thread that threatened Pern. The various colored dragons had differing status and personality types based on color1. (I read the book in 1975).
Game-wise, whether or not this setting inspired Gygax, Arneson, and TSR is unknown, but it's likely given the wide variety of adventure stories, sci-fi, fantasy, swords and sorcery tales, legends, and speculative fiction that inspired and provided ideas for the fantasy game in the first place. Multiple kinds and colors of dragons in the game's lore may be a first for a game, (Blackmoor/D&D) but Pern certainly predated it in literature. That dragons in general were described differently in different story telling traditions for millennia makes the general idea very, very old in the treatment of this iconic creature.
Blame it on Blackmoor
Was it a "first" in D&D as published or from something earlier?
From a post at Dragonsfoot: (Poster Harvard, Fri April 27, 2012, 10:48 am)
It appears that Dave Arneson and Richard Snider were the first to use dragons of different sizes, colors and breath weapons in an RPG. These were in the Blackmoor campaign (1970/1971) time frame (-Harvard- calls it the "proto" D&D era for Blackmoor) which is three years before Dungeons and Dragons was first published.
1From the summary at Wikipedia, which squares with what I remember from the story. Dragons with different colors had differing personality templates.
The dragons come in several colors which generally correlate with their sizes; blue males, green females, brown males, bronze males, and golden females – queens. Bronzes, the largest males, are by tradition the only ones who compete to win the queens in their mating flights. The green females are banned from breeding as they produce only small, less talented dragons. The golden queens are not only the largest dragons, they also hold a subtle control over their dragon communities Weyrs. {Gold dragons did not breath fire as that interferes with breeding -- credit to @MichaelRichardson}
That idea wasn't cut and pasted into D&D. There were no "red dragons" in Pern: they breathed fire /phosgene gas after chewing on certain rocks. Anne McCaffery wasn't writing a game, she was telling a story that took that which was familiar from older story telling traditions -- flying dragons that breath fire -- and folded it into a sci-fi setting in a novel way.
Best Answer
Not all role-playing game have fumbles. In fact, I suspect that were an intrepid soul to catalog every RPG—a daunting if not impossible task—, more RPGs would lack fumbles than possess them. However, many games have optional rules for fumbles for those players who like them, and many games will have specific elements that'll see a deeply flawed attempt yield consequences worse than mere failure despite lacking a general rule for fumbles. So, yeah, while the games you've played have had fumbles, fumbles are by no means a universal.
Possibly the original fumble mechanics
While I'm no role-playing game scholar, Chaosium's Runequest (1978) apparently included fumbles at least as early as 1980 (which is the version I extracted from my shelf, dusted off, and cracked the binding of when I flipped through it). Runequest (1980) has the following section:
(It took a moment to find the page number: they're on the outside upper corner of each page. Pro Tip: If you're laying out a book, don't do that!)
A chart on which one is to roll if a fumble occurs appears soon after.
Jonn Rees apparently ran these numbers both for skill use and the chart. I'm looking at Steve Jackson Games' Murphy's Rules (1988), a collection of comic strips detailing amusing and incongruous game rules from the magazines Fantasy Gamer and Space Gamer (yes, there used to be several gaming magazines!), and John Rees submitted an oddity in 1984 that says
So, even then, while the sheer frequency of fumbles wasn't considered necessarily bad design, it was, at least, considered funny.
Speculation: Why fumbles exist
Fans of role-playing games may view the fictional reality the role-playing game creates as a heightened reality, which I'll call for convenience reality-plus. In actual reality—the one most of us are in, like it or not—, very little that happens matters in the grand scheme of things. In reality-plus, however, everything that happens during the game matters, and spectacle is expected for good or ill. And spectacle during even everyday tasks can lead to comedy or tragedy that is a hallmark of reality-plus.
For example, while training with his Great Axe [sic], Argath of Sartar chops off his own head. That's a thing that probably would not happen in actual reality—very few real-world highly trained axemen accidentally decapitate themselves—, but that sort of spectacle is expected in reality-plus because Argath of Sartar is important, and his training took place during the game.
A game with fumbles tends not to mirror reality because the random number generator that's used has so little granularity. A highly trained archer might shoot himself in the head with an arrow or some other absurdity, but that surely won't happen once every 100 arrows he fires in actual reality! Were there even a 1% chance of every attempt leading to catastrophe in our reality, archery ranges would be sad, sad places, littered with the dead, naked, and injured.
But in reality-plus if those 100 arrows are fired while they matter—during the actual game—, one of those hundred arrows is likely to cause the archer's armor strap to break or make him fall and twist his ankle (those are average results on the Runequest (1980) Fumble Table). That happens in reality-plus because that's spectacular.
That possibility of spectacle makes the game, for some, more interesting rather than more ridiculous. It turns the game from what some may view as a mere simulation into a drama, albeit, in this fan's opinion, in a really forced way.