In no particular order:
The Changing of the Guard - Original Air Date: June 1st, 1962/Episode 102, Season 3
An elderly English literature teacher that goes by the name of Professor Ellis Fowler, who teaches at an all-boys prep school for almost 50 years, is forced into retirement. On Christmas Eve, after teaching generations of students, he wonders if his life's work had any meaningful impact. Feeling lost & ashamed, he wonders back to the campus, with revolver in hand. Before he could attempt suicide, he hears the school bell, which is coming from the deserted classroom building. Mr. Fowler is then visited by ghosts of several boys who were his students, some that had died heroically.
One by one, the boys thank Professor Fowler for the impact he has had on their very important lives. In a way, these lost souls have teached Professor Fowler the most important lesson in life, and is able to help him move onto the next stage.
Come Wander With Me - Original Air Date: May 22nd, 1964/Episode 154, Season 5
A popular musician (Floyd Burney) travels across the state, in order to find inspiration to compose a folk song of his own. Sometime after crossing with a non-helpful shop keep, he comes across one of the local girls in a small town, a beautiful woman by the name of Mary Rachael. She takes interest with Floyd, and after bribing her with "romance & love," he is able to get her to record her song. After ignoring Rachael's instances of the song being about their love, Burney is confronted with Rachael's fiance Billy Rayford, who accuses Burney of attempts to seduce Mary. The men fight, which leads to Rayford's death.
With Mary appearing in black mourning clothes, Floyd confronts her about what's been happening. Mary only responds that it's the order of things, and she then adds lyrics about Rayford's brothers finding Billy's body, swearing revenge. After abandoning Mary, Floyd attempts to seek help from the shop keep, only for the old man to tell him it's too late. In panic, Floyd kills the shop keep and tries to hide behind some old music boxes, with being to play Mary's song on their own. The brothers find Floyd, and promptly kill him on the spot. Some time later, Floyd's tombstone is in the woods, where he had failed to see it earlier.
No Time Like The Past - Original Air Date: March 7th, 1963/Episode 112, Season 4
Two men (Paul Driscoll & Harvey) attempt to use a time machine, with the noble intention to go back in time and alter past events, namely to minimize the lost of human life during the First & Second World Wars. However, their attempts prove to be futile, as no matter how hard they try, they cannot alter the events of human history. From warning the Hiroshima police captain about the atomic bomb to his failed attempts to prevent Lusitania being torpedoed, Paul slowly comes to the conclusion that the past cannot be rewritten, so he then travels to Indiana the mid-19th Century, so he can live an uncomplicated life.
After several events that have transpired, Paul stays at a boarding house. After getting into an argument with another boarder about imperialism, Paul reads a history book about Homeville's schoolhouse will be burned down, due to a lantern ejected from a runaway wagon. After his failed attempt to stop the wagon, Paul dejectedly returns to his own time, coming to the conclusion that one should never tamper with the past.
The Incredible World of Horace Ford - Original Air Date: April 18th, 1963/Episode 117, Season 4
Horace Ford, a toy designer that is obsessed with his blissful memories of his childhood, is having harsh repercussions with his career and marriage. Upon revisiting his childhood neighbourhood, he discovers that nothing has changed, along with the boys he used to play with. After revisiting that neighbourhood for several nights, he realize that this his opportunity to revisit those glory days. After reverting to his 7 year-old self, his old friends assault him, and Ford quickly realizes that his romanticize childhood wasn't was pleasant as he'd thought.
His wife finds him, and after telling him to grow up, Ford returns to his period and age group, with a greater appreciation for his life as an adult.
The Lonely - Original Air Date: November 13th, 1959/Episode 7, Season 1
In the distant future, a man named Corry is sentence to solitary confinement on a distant asteroid for 50 years. During the 4th year of his confinement, he is visited by a spacecraft that regularly brings him supplies & news from the Earth. The Captain has been trying to make Corry's stay humanely tolerable, so during his most recent visit, he decides to bring him an bionic robot (that resembles a female adult) that goes by the name of Alicia.
While he first rejects the affections of this synthetic machine, he realizes she possessed incredible physical and reasoning capabilities. In due time, he begins to warm up towards Alicia. Upon Captain Allenby's return, he informs Corry that he's been pardoned, but they have little time to waste. Since there is only enough room for 15 pounds of luggage, meaning Alicia has to be left behind. Corry frantically tries to convince Allenby that she is more than a synthetic machine. Allenby has little choice, but to "kill" Alicia, by shooting her in the face. As she malfunctions, he drags Corry to the ship, reassuring him that "he will only be leaving loneliness."
Deaths-Head Revisited - Original Air Date: November 10th, 1961/Episode 74, Season 3
A former captain in the Schutzstaffel returns to an abandoned concentration camp to relive the memories of his time as its commandant during the Second World War. Upon gleefully recollecting the memories of the tormented inmates, he runs into one of the camps inmates, a man that goes by the name of Alfred Becker. During their exchange, Gunther Lutze claims that he was only doing his orders from his commanding officer, not knowing that the Third Reich planned on exterminating all the Jews. Becker, however, bluntly tells him the reality of the inhumane treatment of the inmates.
Becker, along with the men that Lutze had mutilated all those years ago, put him through the same horrors they had gone through, though psychological torture. Not long after, Becker's ghost informs the now-insane Lutze that it's only the beginning, as his final trial will be that with God. After being sent to a mental institution, the men that found him try to find some reasoning for how Lutze was driven insane. The doctor, after examining his surroundings, ask's "Why does it still stand? Why do we keep it standing?!"
The Gift - Original Air Date: April 27th, 1962/Episode 97, Season 3
After crash-landing on the planet Earth, just outside a mountain village near the Texas-Mexico border, an alien stumbles into the village bar, bleeding from two gunshot wounds. After the doctor removes the bullets from his chest, the alien (referring to himself as "Mr. Williams") becomes friends with an orphan named Pedro.
Pedro receives a gift from Mr. Williams, who tells him that he'll explain it's contents a bit later. The bartender notifies the army about Williams' location, & after fruitlessly escaping, he is surrounded by local arm enforcement, the villagers, & soldiers. Mr. Williams tries to explain that he comes in peace, telling the populace that a police officer he killed (in which shot him) was an accident. He tells Pedro to show them the gift to the doctor, but the villagers take it from him & set it on fire, claiming it's from the devil. When Williams tries to reach to Pedro, the army guns him down. Sometime afterwards, the doctor picks up the remains of Mr. Williams gift, reading a note that it was a vaccine that can cure all forms of cancer.