American Gods: Mad Sweeney is a male example, he is always angry about something and loves to pick a fight.
Castle: Castle is surrounded by fiery redheads (with varying degrees of redness): his spacy but tough mother, his sweet daughter who isn't afraid to tell him off when necessary, and his police detective partner who is an Action Girl with a gun. In fact, as Beckett has defrosted and become much less icy and abrasive, her hair has softened◊ from a deep red to brown.
Commander In Chief: Vice-President Mackenzie Allen was encouraged by everyone to resign when death by aneurysm got a hold of the President. Instead, she took the Oath of Office, won the country, and was generally a spitfire who shouldered the responsibility of the Presidency without getting drunk on power - and God help you if you stood in her way. Fiery Redhead, indeed!
CSI: Catherine Willows borderlines this, as a strawberry blonde. It's not deep red, but probably got enough red mixed with the blonde to count. And she's got the personality to go with it.
CSI: Miami: Horatio Caine, sometimes. You definitely don't want to get on his bad side. He'll hunt you across however many countries it takes, as the Mala Noches could attest. He didn't exactly seem to have trouble getting women, either, though they kept getting killed for some reason.
Daredevil (2015): Matt Murdock sports reddish-brown hair. (The makeup artists had in fact originally considered going for the bright red hair that Matt sports in the comics, but found that it looked too silly on Charlie Cox, so they had to downplay it to simply applying a slight tint to his natural hair color).
Days of Our Lives: Melanie Jonas (formerly Melanie Layton Kiriakis). Despite being downright saccharine at times, if you get on her bad side, she'll really let you have it. Also, since she's about to gain her sixth love interest in less than three years, she definitely qualifies as an example of Heroes Want Redheads. Her Parental Substitute Maggie also fits this trope.
Defiance: Irisa Nyira, played by Stephanie Leonidas (who is not red-headed in Real Life). This leading to this comment IMDB: "Is it wrong of me to find her more attractive as an alien than the actor behind it?" and the reply, "Proof that redheads are just better?". Irisa is possibly also an example of the "Big Eyes" part of trope Big Eyes, Little Eyes.
Donna Noble, who was probably the loudest companion yet (but that's not necessarily a bad thing). One character refers to her as being "all red hair and fiery".
As well as Amy Pond. Not quite as loud, but just as fiery. Actually lampshaded in the show itself, with the line, "Loves a redhead, our Doctor!"
ER: Whatever Kerry Weaver's numerous flaws were, no one could say she was a wimp or a pushover.
Ferienheim Bergkristall: Ginger-haired Susanne Pieper, who though obnoxious is still found to be cute by Hans-Günther.
Fraggle Rock: Red, with her extreme tomboy nature, her... very high self-esteem, and her dominant personality (which itself causes numerous conflicts), plus her own explicitly stated desires ("The Tale of the Triumphant Princess" anyone?).
Law & Order: Special Victims Unit: When Assistant District Attorney Casey Novak isn't on the scene with guns blazing and taking a hands-on approach to the cases, she is in softball batting practice or bicycling to work.
Magnificent Century: Aleksandra/Hürrem. Almost the first thing she does in the series is to grab a breadknife and attack the slavers who are holding her and her countrywomen captive.
Melrose Place: All of the redheaded women on Melrose Place (at least eventually in Kimberly Shaw's case), but most noticably Sydney Andrews, the troublemaking, prostitute/stripper younger sister of Jane Mancini.
And this was not just reserved for women; there was also Dr. Bret "Coop" Cooper, as well.
My So-Called Life: Central character Angela Chase evokes this trope by dying her hair "crimson glow". Former best friend Sharon Cherski is a lot calmer and more manageable than Angela, but she still easily fits the trope. Same goes with Hallie Lowenthal, the series' resident adult Fiery Redhead.
Picket Fences: As seemingly the sole female cop in the boys' club that is the Rome Sheriff's Department, Deputy Maxine 'Max' Stewart definitely fits the prototype of the fiery redhead. She's determined, passionate , ambitious, outspoken at times and quick to anger.
Series/Reba: Both the title character (with her anger at her ex-husband's second wife giving her a heart attack at her daughter's wedding) and her Deadpan Snarker teenage daughter Kyra fall firmly into this trope.
Rescue Special Ops: Heidi. There are quite a few examples of this but one that stands out is when the Cops and Firies trick Chase out of RSO's equipment after he is put on light duties, Heidi uses her cleverness to trick both into giving the equipment back by giving them the information about a nurses party, she fails to mention that it's a male nurses party.
Revolution: Emma in the episode "Home". She wasn't a combatant like most other characters, but she didn't hesitate to get in Big Bad Monroe's face and call him out on his actions. She also attempted to make an honest appeal to his better nature. It didn't work, but he did admit that he wants to be the person she remembers so badly. She was his girlfriend at one time, so it gave them a special connection. Then, when he tried using her as a hostage, she didn't panic. In fact, she ended revealing that she gave birth to his son at some point in time and sent him away. Before she can tell him where, she got shot and killed. She had a major impact on Monroe from beginning to end.
Salem: Anne Hale, one of the few people to speak out against the witch hunt.
Selfie has a downplayed example in main character Eliza (played by Karen Gillan). While not exactly fiery, she is rather emotional, impulsive, and flighty.
The Sentinel: We have Naomi Sandburg, who seems like a peace-loving ex-flowerchild, until you threaten her son; Jim's ex-wife Carolyn; and Megan Connor, the Antipodean Amazon.
Sleepy Hollow has Ichabod Crane's wife Katrina. Abbie put it best after Ichabod despairs that he should have stopped Katrina from staying with the Headless Horseman to spy on Moloch's plans.
Abbie: She's a grown woman, a witch, and a redhead. You couldn't have stopped her if you tried.
Smallville: Tess Mercer. You do NOT want to get in her way or get her angry.
Spellbinder: Ashka, the callous, mean, chronically double-crossing and power-hungry bitch.
Star Trek: Deep Space Nine: Major Kira Nerys. Former Bajoran resistance fighter, current second-in-command of Deep Space Nine, and with an always fiery personality. She once beat the shit out of a serial killer while the equivalent of nine months pregnant. The personality type is implied by Chief O'Brien in the pilot to be a trait common in Bajoran women (probably referring back to Ro Laren, whose role the character of Kira was created to replace).
Star Trek: The Next Generation: Dr. Beverly Crusher - do not piss her off or you will find yourself dropped by Klingon martial arts faster than you can say 'hypospray'.
Star Trek: Voyager: Captain Janeway, though, as she's The Captain, she doesn't have to lose her temper, just give them the Glare of Death. Strong, very expressive, and touchy in her body language even though she's a Celibate Hero, and quickly gets badass on anyone who threatens her ship or crew.
Stranger Things has an interesting bag for redheads, as of Season 3 there have been three redheads: Barb Holland, Maxine "Max" Mayfield, and her mother. As a Tomboy who playfully calls her boyfriend "Stalker" and pushes against the norms for Hawkins girls while contending with an abusive stepbrother, she plays with this but proves to be as resilient and strong she she aims to be. Her passive mother has the same haircolor but averts this trope as a Useless Bystander Parent while Barb Holland rarely expresses anything more hotter than annoyance at her friend cavorting with a bad crowd and becomes a tragic aversion.
WWE: Amy Dumas (Lita) was a pretty decent personification of this, being flashy, outgoing, and pretty willing to jump in the middle of anyone who crossed her, male or female.
Sgt. Krystina Breeland of X Company is not so much fiery as just badass. She's generally calm and collected, but is not adverse to kicking some ass and even torturing a prisoner for information when the situation calls for it.