A part of the charm of the Star Trek franchise is how many new alien species it introduced over the years. The rich background of the world continues to attract both old and new fans. Of all the Star Trek species, the Klingons remain one of the most popular ones among fans.
While their culture and way of life are vastly different from humans, as Klingons are warriors by heart and put a lot of emphasis on honor and conflict, they're still able to work with other species if the circumstances are right. Many Klingons appeared in Star Trek but only a few became downright iconic.
5 Klaang
While casual Star Trek viewers might not be as familiar with Klaang as with other Klingon characters, he still holds a special position in Star Trek history. His was the first case the Klingons ever interacted with humans on their home planet, Earth. Unfortunately, the meeting didn't go so well. Klaang was running from the Sullibans and was shot by a local farmer who considered him a threat.
Fortunately, Captain Jonathan Archer offered to take Klaang back to his planet which later helped the USS Enterprise in their mission. It was the beginning of diplomatic relationships between humans and Klingons which ultimately, two centuries later, led to Klingons serving in the Starfleet.
4 Kahless
While not playing as major a role in the story as other Klingons, leaving Kahless out would be a mistake. He was the first Emperor of the Klingon Empire and Klingons continued to honor him and follow his example even thousands of years later. As such, Kahless became similarly instrumental to the Klingon culture as the philosopher Surak was for the Vulcans, for example. Kahless personified everything that the modern day Klingons admired and wished to be like.
He was brave, cunning, intelligent, strong, and an excellent warrior. As such, he managed to do something no other Klingon succeeded in doing after him for centuries. Kahless united all the Klingons and in doing so, effectively created the Klingon Empire. Kahless's story is fascinating as it shows that the Klingons have a mythology that's just as rich as with humans and other Star Trek species.
3 Ash Tyler
Star Trek: Discovery gave new appearance to the Klingons, something that didn't sit well with some of Star Trek's longtime fans. However, at least the audience got to see more of the Klingon culture and the way they operate when waging a war. Ash Tyler was an unusual Klingon. He was transformed into a human to infiltrate the ship Discovery and find out their secrets.
While in disguise and unaware of his true nature, Ash had grown close to Michael Burnham. So she was devastated when she learned the truth and Ash tried to kill her. His story was tragic at times, proving that being torn between two different worlds is no easy task for anyone, Klingons included. The story's dark undertones also helped characterize the show's overall serious tone.
2 B'Elanna Torres
B'Elanna easily became one of the most popular characters of Star Trek: Voyager. Just like some of the most iconic Klingons and Star Trek characters in general (such as Spock), B'Elanna had a dual heritage. She was the daughter of a Klingon mother and a human father, something that had a major impact on her life and that the show took the time to explore in greater details. B'Elanna was an excellent engineer and quick on her feet but struggled with her temper and following orders from those she didn't respect.
As such, it was initially difficult for her to integrate into the crew of the ship Voyager, but she managed it in the end. Without B'Elanna's technical genius, it's doubtful whether Voyager would have made it back into the Alpha Quadrant. B'Elanna was not only successful in her work but in personal life as well. She got together with Tom Paris, they got married and had a daughter called Miral.
1 Worf
Unsurprisingly, Worf remains the most influential Star Trek Klingon to this day. He broke a record when he joined Starfleet as the first Klingon ever. Not all Klingons were happy with this decision, though, and they weren't afraid to make their displeasure known whenever they met Worf. He served under Captain Picard and became the chief of security which suited Worf well, considering his fighting prowess and the fact that he could look threatening if he so decided. Worf rose through the ranks and became a lieutenant commander, proving he was just as capable as any other Starfleet officer.
He later served on the space station Deep Space Nine where he got together with his future wife, Jadzia Dax, who was a Trill, proving yet again that Worf wasn't by any means bigoted. And even later, Worf worked for the Starfleet Intelligence. He was a close friend of Picard and built a friendship with other crew members as well. Worf was not only an accomplished Starfleet officer, but also a talented Klingon warrior, and as such, he represented the best of both worlds.