Cool Teacher

A teacher...who is cool. They motivate their students to learn (possibly in fun ways that are actually fun), laugh at the Stern Teacher and Misplaced Kindergarten Teacher behind their backs, protect their students from the Sadist Teacher and oppose the Evil Teacher and Dean Bitterman at every turn. Their consistently good results might protect them from being a Fired Teacher, but this isn't a given. A lot of these end up being The Mentor either way.

Often a Foil to the Apathetic Teacher.

Supertrope to: Psychologist Teacher and Badass Teacher

Anime and Manga

 * Shizuka Nekonome in Rosario + Vampire is one of the few teachers who happens to be generally nice to everyone, enthusiatic about her job and helping her students learn, and actively encourages her students to participate in extracurricular activities.
 * She does have a nasty habit of scratching her students though.
 * The entire premise of Great Teacher Onizuka.
 * Takamichi of Mahou Sensei Negima is often viewed as this. Negi kind of counts.
 * Monsieur Dufarge, Sara's French teacher in Shokojo Sera, is a good example, and ends up being a father figure to her. Of course, this leads to inevitable consequences, given the sort of series it is.
 * Fruits Basket (manga only) has "Mayu-Chan-Sensei" as the girl students call her. At one point she pretends to get angry, then grins and tells them to refer to her as "Great Teacher Mayuko".
 * Yamaguchi Kumiko.
 * Mr. Colbert from The Familiar of Zero.
 * Komoe-Sensei from A Certain Magical Index
 * Sumiko Kobayashi from Detective Conan, also pretty enough to qualify as a Hot Teacher.
 * Kakashi from Naruto. More like Badass Teacher.
 * Misaki from Misaki Number One.

Film

 * John Keating from Dead Poets Society.
 * Mr. Freddy Shoop in Summer School. Maybe a little too cool at times, but justified in that he's just the gym teacher who was forced to teach remedial English or lose his job.
 * To Sir, With Love.
 * Professor William Hundert of The Emperor's Club
 * Lou Anne Johnson from Dangerous Minds
 * Jaime Escalante, from Stand and Deliver, which is based on an awesome true story (see Real Life, below).
 * Dewey Finn in School of Rock
 * Mr. Freeman from "Speak"
 * Charles Xavier in X Men First Class
 * Glenn Holland in Mr. Holland's Opus
 * Jack Griffith (played by Thomas Haden Church) in Easy A, at least through Olive's eyes. Starts one class with a rap song, although he immediately stops, claiming that doing that is disrespectful.
 * Mary in The Muppets, such that her students simultaneously admit they'll miss her during their two-week Spring Break.

Literature

 * Mr. G from the books of The Princess Diaries.
 * Sylvia Barrett from Up The Down Staircase.
 * Harry Potter has Professor Lupin in Harry Potter and the Prisoner of Azkaban (in his later appearances he was no longer a teacher) and  Moody in book 4. Hagrid also counted while he was care of magical creatures teacher (although his lessons got a bit dangerous) as well.
 * In the film of Harry Potter and the Order of the Phoenix, when Harry himself becomes a teacher of sorts for Dumbledore's Army, Daniel Radcliffe suggested that Harry dress somewhat like Lupin in those scenes because he was the teacher he liked best and most wanted to emulate. Awww.
 * Technically, all of the teachers qualify, with the exceptions of Umbridge and the Carrows.
 * Susan Sto Helit counts, by Thief Of Time. She takes her students on field trips to battlefields and other continents, and has bogeymen and Death himself come in to talk to them. She quite possibly overlaps with Badass Teacher as well.
 * Honoria Bulstrode, headmistress of Meadowbanks, from the Agatha Christie novel Cat Among the Pigeons. She's not overly strict, but she seems to have an almost telepathic knowledge of everything that goes on at her school. Eileen Rich, the English teacher, also qualifies.
 * In addition, Miss Bulstrode's friend Miss Emlyn from Halloween Party. Miss Emlyn actually figures out who the killer is before Poirot does, though she doesn't have enough evidence to go to the police, and Poirot consults her on several details of his plan before executing it.
 * In the 6th Ciaphas Cain book, Ciaphus seems to have become one of these (he admits to being more relaxed than the other teachers and seems more than willing to take his trainee commissars into the field to get some experience).
 * Aristo in The Roman Mysteries in the tutor of the four main character. He doubles as a Hot Teacher.

Live-Action TV

 * In Boy Meets World, there was a cool teacher named Mr. Turner, and a "square" one, Mr. Feeny, who actually turns out to be something of a cool teacher and mentor to the students himself.
 * In one episode Eric takes over teaching a citizenship class for immigrants and turns out to be a rather cool (and incredibly gifted) teacher himself.
 * Also, in Boy Meets World there was an episode when they were in college where they had a "cool" young professor, played by Fred Savage (Ben's real-life older brother). This episode kind of questions the trope because the professor doesn't respect boundaries—he tries to sleep with Topanga.
 * Max Medina from Gilmore Girls.
 * Grange Hill had one of these at least once every season. The Stern Teacher headmaster even became one as he neared retirement.
 * The entire premise of Hangin' With Mr. Cooper.
 * Howard Hesseman's character in Head of the Class.
 * In My So-Called Life, a challenging but inspirational teacher has a brief stay at the school and seems to be the only teacher to care that Jordan can't read. Ultimately he's forced out when some skeletons in his personal life come to light, leaving his former students confused.
 * The short-lived Sitcom Nick Freno, Licensed Teacher
 * The short-lived Sitcom Mr. Rhoades
 * Mr. Rooks in the Veronica Mars episode Mars v. Mars is this.
 * Danny Hanson in Boston Public
 * Mr. Schuester in Glee is definitely this. Bonus points for being one of the main characters in the show.
 * Emma Pillsbury also has shades of this, however she's just the guidance counselor and is a tiny bit to occupied with her own problems.
 * Substitute teacher Hollie Holliday turned out to be a very cool teacher and was considered even cooler than Mr Shuester. However, she took it too far and let Mercedes sabotage Sue's car and was then unable to deal with the consequences.
 * Dr. Thomas Oliver in Power Rangers Dino Thunder. Careers prior to teaching include superhero (more consecutive years doing so than anyone else on the planet), professional race-car driver, and mad scientist (he made robot dinosaurs). Won several martial arts competitions back when he was in school. Fit all of his college education, racecar driving, and mad science career into seven years. Has finally cut his hair into a cool hairstyle.
 * Professor Z from Black Hole High. You wish you'd paid more attention in science class.
 * Rod Belding from Saved by the Bell
 * Possibly a subversion... Mr Belding tried to be the cool teacher, but was generally the Reasonable Authority Figure. It was only when a third party entered the scene that Belding would team up with his students and let his Cool Teacher flag fly.
 * A repeated sketch in Armstrong And Miller (the Channel 4 version) spoofed this. The skits starred a really Cool Teacher who would use his unorthodox teaching method and passion to teach life lessons and make sure his students get the most out of their education... until the bell would ring, at which point he would become the ultimate Apathetic Teacher, immediately pulling out a newspaper, sitting down and telling his students to "fuck off", in the process completely abandoning or even directly contradicting whatever message he'd been trying to teach mere seconds ago.
 * Prof. Whitman from Community tries to be this. Depending on your taste he may or may not be successful.
 * Protagonists Trevor Chaplin and Jill Swinburne from The Beiderbecke Affair are both regarded as this by their pupils, especially Jill.
 * Ximena, Susana, and Rene from Carrusel.
 * Syrio Forel of Game of Thrones, Arya's "dancing master", who instructs her in both Braavosi swordfighting and advanced scenery-chewing.
 * Dr. Dupree in The Famous Jett Jackson has elements of this. He seems to be your typical English teacher, but he does, on occasion, do something fun. In one episode, Jett screws up royally with his family, at school (by reading Poe's Raven to a rap beat, causing Dupree to shut him down and claim he's disrespecting the author), and friends. He then appears to end up in a Groundhog Day Loop. On his third iteration, he manages to get everything right. Then it turns out to have been All Just a Dream, except the first iteration, naturally. Except that things actually get better. His friend is no longer pissed at him, realizing he was right. His great-grandmother and his father admit they overreacted. At school, Dr. Dupree also admits that Jett's "performance" wasn't as bad as he initially thought. In his mind, Jett tried to mix Poe's poetry with the "urban poetry of rap", which was very popular with the students.

Video Games

 * Mrs. Potsdam from Magical Diary: Horse Hall, in stark contrast to Stern Teacher Mr. Grabiner.
 * , of all people, takes on this role to a class of biotics at Grissom Academy in Mass Effect 3 provided she survived the second game.

Western Animation

 * The Magic School Bus has Ms. Frizzle. She has a pet chameleon, her school bus can go anywhere in time or space, and nothing ever fazes her.
 * An episode of Recess had a former student (and rival of Sadist Teacher Ms. Finster) return to the school to work as a teacher. By the end of the episode he's reconciled his love of science with his aversion to being boring and became one of these.
 * Also, the mysterious Mr. E, a substitute teacher who wins over the entire class with the exception of TJ, who's appalled at how quickly they forgot about Ms. Grotke.
 * Miss Grotke's a pretty cool teacher herself.
 * Substitute teacher Mr. Bergstrom from The Simpsons episode "Lisa's Substitute."
 * Also Zachary Vaughn from "Bart Gets a 'Z'". At least until he gets drunk.
 * Monk Gyatso of Avatar: The Last Airbender teaches Aang to airbend pies at other, meditating monks. While the other senior monks at the Southern Air Temple take a more disciplinarian stance and want to accelerate Aang's training because of the war on the horizon, Gyatso insists that he have a happy childhood.
 * Don't forget Uncle Iroh. Just watch any scene where he's teaching Zuko a lesson in fire-bending or general life lessons. He is more of a father to Zuko than his actual father.
 * Quetzal of Dragon Tales. His substitute, Ms. Tip, also counts.
 * Miss Finch on Birdz is generally supportive of Eddie. In one episode, she allows him to shoot a video essay instead of writing one, to support his love of filmmaking.

Real Life

 * Many people will have "that one teacher" who is just plain awesome and does things his/her own way.
 * Purportedly, Something Awful Goon/high school science/forensics teacher Gene Splicer is this: "Who was the one who brought the maggots so the students could mess around with them? Me!" The other known teacher-goonette, English professor(?) Jidohabankai (this is almost certainly wrong) is more of a Sadist Teacher With A Heart Of Gold (she does terrible things to cell phones that dare to ring during classtime).
 * Jaime Escalante, made famous by Edward James Olmos' portrayal in Stand and Deliver, was a Bolivian immigrant who came to Los Angeles to teach computer literacy at an inner city school. Only, when he arrived, there were no computers, so instead he started teaching math, including starting an AP Calculus class. Despite numerous naysayers, his AP class consistently had the highest test passage rate in the country (so high that at one point they were investigated for cheating, but were exonerated). He was so beloved by his students that they stole his car in order to fix it up for him (many of his successful students were former delinquents). On the side, he taught remedial math and an English class for immigrants at night.
 * Carl Sagan. Many of his own students are now big-time celebrity scientists in their own right. Neil De Grasse Tyson might be the most famous example. Bill Nye is another.