Hive Series has Otto and Laura, who are separately shown to lack driving skills. In book six, the team rushes to keep Laura from driving a car when they go to Europe, and when the Alphas have to learn to fly helicopters, everyone shies away from partnering with Otto, who apparently vaporized every simulated character in a thousand foot radius last time they did the exercise.
Tom Clancy's novel Rainbow Six has a hilarious Chase Scene sequence where a bunch of terrorists invoke this trope to get away from a blown mission, and John Clark tells the driver of his vehicle to avoid this trope, while still trying to keep up with the Drives Like Crazy terrorists.
Miss Havisham is fond of driving at full pelt through a city, nearly running over, well, everything. She does drag races on a fairly regular basis, and some of the stunts she pulls off in the real world would be impressive for NASCAR drivers. Lack of skill is not the issue here.
Jordan Baker in The Great Gatsby states that she trusts other drivers to get out of her way. Daisy Buchanan also has an episode when she drives while emotionally distraught and kills Myrtle Wilson.Women Drivers, huh?
The eponymous women herself might be a decent driver, but she is death on cars. Hers get destroyed almost once a book, albeit usually for reasons beyond her control such as bombs and fires. Ranger, Stephanie's mentor/UST generator, is cool with giving her cars as he writes it off as 'entertainment'.
On the other hand, Grandma Mazur, once she finally learned to drive, managed to rack up enough moving violations to lose her license. In five days. The few who've ridden with her frequently complain about problems like whiplash from abrupt stops, etc.
Valentine Michael Smith of Robert A. Heinlein's Stranger in a Strange Land appears to drive like this. It's actually perfectly controlled, because he's stretching his sense of time so that he sees everything in slow motion. It's mentioned to be very scary to watch, but perfectly safe.
Amelia Peabody Emerson and her husband Professor Radcliffe Emerson, in Elizabeth Peters' mystery novels. To be fair, cars were a novelty at the time, and neither ever had any formal driver's training, but Amelia's daughter-in-law tried to give her a lesson — and later made excuses never to ride with her again. As for the Professor, his style of driving is "floor it and hit the horn a lot" (not a quote from the books, but accurate).
David Drake's RCN series has a standing joke that nobody can drive an aircar. By some count, seven named characters and a couple of redshirts have claimed this ability and at best they get there with severe dents. Rather makes you wonder why a spaceship that hasn't always got room for the guns bothers to carry one.
Animorphs: Marco's bad driving is a Running Gag established in the first book, where he can't even drive a golf cart without crashing into things. Naturally, whenever the team needs a car, he somehow winds up behind the wheel. (Note that, like the other Animorphs, Marco is thirteen at the start of the series, though he insists he's an expert thanks to video games.) Eventually he gets to drive in a US National Guard Abrams Main Battle Tank. (He runs over Chapman's house in said tank on a lark. He needed a parking space, okay?)
Question: Where does the driver of an Abrams park? Answer: Wherever he wants!
Marco: I can't drive with you screaming in my ear.
Jake: You can't drive at all!
In Book #30, it turns out he inherited this from his mom, and Visser One isn't any better.
Tobias turns out to be an even worse driver than Marco, who promptly calls him on it. He deserves a little more leeway than Marco since not only does he not normally have arms. He's not usually a two metre tall dinosaur alien driving with his head stuck out of the sunroof.
Jurgen, the aide of Ciaphas Cain, Drives Like Crazy... And his vehicle of choice is an upgunned Salamander, a 33 tonne heavy tracked scout tank. Road signs, telephone poles, parked vehicles and anything else that is unfortunate enough to occupy the shortest route between Jurgen and his current goal has a nasty habit of getting flattened, although he stops short of actual vehicular homicide (at least to Cain's knowledge). The only person in the grim future of the 41st millennium capable of coaxing a vehicle the size of a small bus down back alleys or parallel parking it, the effects of his driving to his passengers are best left unchronicled.
The Traitor's Hand does actually feature Jurgen demonstrating vehicular homicide with a 33-ton tank. It was against heretics, so nobody really minds... heretics who happened to be inside a house at the time.
This trait comes in handy a lot, as Jurgen WILL get you where you need to go very quickly. And if the vehicle you are in is ambushed, there is no better man to have behind the wheel. He also takes warnings that the upcoming road in a post-urban-warfare region is impassable as a challenge, and when told to "get onto the shuttle now" he takes it quite literally, driving up into said shuttle's bay at full speed. And stopping the tank on a dime.
A testament to Cain's competence is that he's used to Jurgen's driving enough to stand on the back and man the heavy bolter, which is a heavier weapon than standard.
While nowhere near Jurgen's standards (or lack thereof), Mari Magot seems to have developed a reputation for this — if Cain identifying her as the driver of an APC by it running over a Tyranid Lictor is any indication.
Doctor Plemponi, principal of the Colonial School in James H. Schmitz' Trigger Argee novel Legacy, is a classic example of this trope. Only the fact that all aircars in the setting are equipped with computerized safety overrides and collision-avoidance autopilots keeps him from committing mass murder every time he gets behind the controls. Even with the best technology can manage, "Plemp" still managed to land his aircar in front of the targets on the outdoor firing range during a live-fire drill. He then proceeded to fly the wrong way at full speed down a one-way traffic airlane, and when this fact was pointed out to him deliberately forced the oncoming aircar to veer off rather than correct his course. God only knows how much carnage would have ensued if he'd had more than one scene in the novel.
In Dan Abnett's Gaunt's Ghosts novel Ghostmaker, Ortiz has a tank driven into headquarters, scattering drilling soldiers and knocking all sorts of things astray. Then, he was inspired: a superior officer had ordered him to fire where Gaunt's Ghosts were, killing hundreds of them; Gaunt had attacked him; and the superior officer was looking to courtmartial and shoot Gaunt. Having gotten there quickly, Ortiz filed a report claiming that his injuries sprang from his own guns' recoil.
The Knight Bus from Harry Potter. Granted, obstacles (including houses) jump out of its way, but even so.
The only thing about Edward Cullen that scares Bella is his driving.
Or any of the Cullens, actually. They all have Super Speed, so driving at human speeds would seem "slow" to them.
They, as well as the Quilutes, are effectively immune to the destructive effects of car accidents on the human body. So they have an excuse.
Max the Silent, in the books about outlaw private eye Burke by Andrew Vachss. The problem is that Max, who has a reputation as a major badass, thinks that people will move aside for him on the road as well as on the sidewalk.
In Maximum Ride, narrator Max drives a van into a sedan at 60 mph the second time she gets behind a wheel — with her family, including an eight-year-old, aboard. To be fair, she was attempting to teach herself how to drive. It just didn't turn out well.
Nudge: I didn't know a van could go up on two wheels like that. For so long.
Lensman. Rigellians are Blind Seers (in place of sight and hearing, they have extra-sensory perception and telepathy) with tough hides that muffle their sense of touch. One minute in a Rigellian automobile (read: extremely powerful but also extremely loud) has been known to drive normal humans insane. A specially-armored and screened protagonist manages to survive the ride, but comes out at the other end severely traumatized. The alien driver is later surprised at this, because he was driving "with the utmost possible care and restraint" (for his species). Meanwhile, he (the following text is a direct quote from First Lensman):
Swung around a steel-sheathed concrete pillar at a speed of at least sixty miles per hour, grazing it so closely that he removed one layer of protective coating from the metal.
Braked so savagely to miss a wildly careening truck that the restraining straps almost cut Samms' body, spacesuit and all, into slices.
Darted into a hole in the traffic so narrow that only tiny fractions of inches separated his hurtling Juggernaut from an enormous steel column on one side and another speeding vehicle on the other.
Executed a double-right-angle reverse curve, thus missing by hair's breadths two vehicles traveling in the opposite direction and one in his own.
As a grand climax to this spectacular exhibition of insane driving, he plunged at full speed into a traffic artery which seemed so full already that it could not hold even one more car. But it couldójust barely could. However, instead of near misses or grazing hits, this time there were bumps, dentsólittle ones, nothing at all, really, only an inch or so deepóand an utterly hellish concatenation and concentration of noise.
Crowley of Good Omens has generally little regard for speed limits, being able to use his demonic powers to dissuade traffic cops and keep his car dent-free. He attempts to maintain traffic laws once and gets locked in Apocalyptic gridlock before reverting and pulling up on the sidewalk.
Perry Mason. It's a Running Gag that he breaks a bunch of traffic laws just to get to places (normally crime scenes). Apparently, Della Street can be just as bad when the urgency arises.
Doodah Day. A pixie who nearly kills Holly Short with a construction vehicle, temporarily reduces Mulch Diggums into a quivering pile of nerves with his piloting of a LEP transport pod, and gets a toy car up to sixty miles per hour — indoors? Breaking the speed limit indoors. He must be Jeremy Clarkson...
Mulch Diggums himself could count:
Holly: What on earth were you doing, Mulch? The computer says you came all the way down here in first gear. Mulch: There are gears?
Mulch's driving technique is described earlier in the book as being "focus on the wheel and the pedals, and ignore everything else." He also assumed the shuttle had an automatic transmission.
Fitz, from the Doctor Who Expanded Universe books, sometimes seems to be a decent driver, and sometimes "crunch[es] the gear stick", crushes azaleas, "let[s] the car shoot backward", skids, and drops a Cluster F-Bomb for half the drive before stalling rather than parking. This particular frightening exhibition was in a car built around when he was born, and he was making a getaway from someone who'd just been holding the Doctor at gunpoint, but still. He never seems to be able to get behind the wheel of a car without incident.
In Kingdom Keepers, Wayne is described as such, noting that a short drive nearly ended with a wreck several times.
In 30 Seconds Over Tokyo when the downed airmen are smuggled out of China, they are driven part way by a driver they call Charlie. He writes that in Charlie's mind, the brakes come third in importance. First comes the horn, then the steering wheel, and only then come the brakes.
In the Aubrey-Maturin series of novels, Diana drives like this in her horse-drawn carriage. It's universally considered terrifying, even by Aubrey himself, although she is an exceptionally good driver. When the sailors try driving, on the other hand...
John Thorpe in Northanger Abbey is a particularly reckless driver, terrifying poor Catherine Morland out of her wits when he takes her for what is supposed to be an enjoyable carriage ride. Granted, we only see the incident from the viewpoint of a genteel English girl, but she does comment that other drivers are much, much more sensible.
Ellie Linton from The Tomorrow Series. She learned her driving on her station's back paddocks, using Land Rovers and "paddock bashers" (unlicensable beaters) but still...
It's a Running Gag in the VI Warshawski novels that Vic's best friend Lotty is a holy terror as a driver; Vic even says at one point no sane person would let Lotty behind the wheel.
Granny Weatherwax, in the Discworld novels, believes it's everything else's job to move out of the way of her Flying Broomstick. This philosophy extends to birds, other witches, trees, tall buildings, clacks towers and mountains. And, because this is Weatherwax we're talking about, they do. Birds have quickly evolved to fly on their backs so they can watch out for her in the sky. It's something of a minor plot point when public perception of witches as Humanoid Abominations has wavered, leading to her almost getting run down by a cart if she hadn't been tackled off the road in time, so used is she to being the one people go around.
In Kate Daniels, this is one of the defining characteristics of Dali Harimau. As she has a shapeshifter's Healing Factor, she considers crashing to be merely inconvenient. Her passengers and nearby pedestrians disagree.
Jim: You're legally blind, you can't pass the exam to get a license, and you drive like shit. You're a menace.
Regarding Lord Ivan Vorpatril we get this exchange:
Gregor: So, Lord Mark, what do you think of Vorbarr Sultana so far? Mark: It went by pretty fast. Gregor: Dear God, don't tell me you let Ivan drive.
In the later novel Memory, it is revealed that Ivan and Miles had a reckless driving competition as teenagers and Miles won decisively. By flying an aircar down a winding narrow canyon at over 100 mph with his eyes closed. When looking back on that period of his life as an older man, Miles concludes that only direct divine intervention kept him and Ivan alive long enough to reach adulthood.
Augustus of The Fault in Our Stars, due in part to his having a prosthetic right leg that prevents him from feeling the subtleties in pressure needed for non-jerky driving experiences. Hazel suspects that the examiner who licensed him (on the third try) only passed him as a "Cancer Perk".
Also Alaska Young from Looking for Alaska by the same author. Though she doesn't have the prosthetic leg excuse.
1632 has Hans Richter, whose approach to defensive driving can be summed up in the maxim "the best defense is a good offense". Or: "Nobody lives forever so why not get where you're going?" Then he discovers airplanes....
John Bankes, in the Father Brown story "The Man with Two Beards".
Phryne Fisher. Her maid and companion Dot takes to routinely screwing her eyes shut and keeping them shut whenever she has to drive somewhere with Phryne.
In John W. Campbell's story "The Brain Pirates", Terruns and all the residents of the tenth world's satellite come off as crazy drivers to the Terrestrial heroes. It's mentioned that their vehicles only go about twenty miles an hour, but thanks to the high gravity there's a lot of traction, and stopping can be very abrupt.
In Tanya Huff's The Enchantment Emporium, it alludes to Auntie Catherine driving like crazy because she charmed her car to act like something from NASCAR. Charlie also drives like crazy in one instance, but that was more of a result of driving said car during an impromptu interrogation from her to her passenger. The sequel The Wild Ways confirms that all the Aunties drive like crazy.
In the October Daye series, Toby's fetch May is a terrible driver. In One Salt Sea, Toby has to ask May to drive Toby's car somewhere, and May demands to know if she's a doppleganger, since the real Toby would never trust her with the car.
Meg Cabot's 1-800-Where-R-U series has sixteen-year-old Jess Mastriani, who freely admits that she likes to go fast, which is part of why she's failed the test to get her driver's license more than once (though she does have a learner's permit). Her wildest ride comes in the fourth book, when she drives a hotwired truck through the snow and ice, jumping a six-foot ravine in the process. After actually hitting town, she commits "twenty-seven traffic violations" en route to the hospital, and crashes through the doors of the emergency room. One of her passengers, before going off to surgery (of an injury sustained before getting in the truck), calls her "the worst driver I have ever seen". She's mellowed out by the events of book 5 though.
Uncle Parker from Helen Cresswell's Bagthorpe Saga drives so recklessly that in the first book the Danish au pair he's delivering to his brother-in-law's family shows up in tears.
Ingrid Brady, the anorexic monk and government spook of the comic neo-noir Get Blank, certainly qualifies. Not everyone will play chicken with a bunch of Satanist gunmen.
Salt in the Penny Parker series. Penny has her moments, too.
In The Nekropolis Archives, one of Matt's friends is a demon cabdriver named Lazlo. He regularly drives through crowds at full speed, with the expectation that anyone in his way will get out of it or get run over.
"Surprise me, Lazlo," I said, "and try not to drive like a maniac for a ch—" That's as far as I got before Lazlo slammed on the gas and I was thrown back against the seat.
The Mote in God's Eye: From a human standpoint, Motie Engineers drive like crazy. From the engineers' point of view, the only sensible way to drive is to make efficient use of every inch of roadway, and they've got the reflexes to do so.
Ngaio Marsh's Agatha Troy from the Inspector Alleyn Mysteries series tends to drive her van through the countryside in a manner that most of her (well-bred) passengers ask her if it would be all right to take over driving. Her TV incarnation, played by Belinda Lang is arguably worse, driving said van worth of the infamous Moose Test. Curiously, the only one not bothered by her driving is Alleyn himself.
In Another Note, Beyond Birthday boasts that he has never submitted to any person, or even to a traffic signal. The one time he is seen driving, the trope is justified, because the car he's driving is stolen.
John Thorpe in Northanger Abbey has a Regency version of a Rice Burner with his "curricle-hung gig." Though its performance doesn't live up to his boasting, it still terrifies Catherine and he ignores her requests to let her off.
In Persuasion, Wentworth jokes at one point that he hopes his sister Sophie won't have to climb out of a ditch again, as his brother-in-law Admiral Croft is apparently not as good a driver as he is a sailor.