Star Trek (1966-1969)

Here are my favorite episodes of the original Star Trek, way ahead of its time and still my favorite science fiction television series.

The Naked Time (Sep. 29, 1966): Arriving in orbit around planet Psi 2000 before its imminent breakup, a landing team beams down to find that all members of the resident research team have died under bizarre circumstances.
What Are Little Girls Made Of? (Oct. 20, 1966): Nurse Christine Chapel is reunited with her old fiancé, Dr. Roger Korby, on Exo III, but the scientist has plans for Captain Kirk and the Federation.
The Menagerie (Nov. 17 & 24, 1966): In the only two-part episode of the original series, the U.S.S. Enterprise and her crew are diverted by a signal from her former captain on Starbase 11. When they arrive they find Captain Christopher Pike, who is severely crippled by radiation burns, confined to a moving chair and his ability to communicate limited to the answers "yes" and "no."
Balance of Terror (Dec. 15, 1966): The Enterprise must decide on its response when a Romulan ship makes a destructively hostile armed probe of Federation territory.
The Galileo Seven (Jan. 5, 1967): In this flawed but excellent episode, Spock commands a stranded landing party when their shuttlecraft is marooned on a planet with hostile natives.
A Taste of Armageddon (Feb. 23, 1967): On a diplomatic mission, the crew visit a planet that is waging a destructive war fought solely by computer simulation, but the casualties are all too real.
This Side of Paradise (Mar. 2, 1967): Expecting the colonists of Omicron Ceti III to be dead after three years of exposure to deadly Berthold rays, Kirk and Spock are surprised to find the colony alive and flourishing.
The Devil in the Dark (Mar. 9, 1967): The Enterprise arrives to investigate reports of an unknown creature deep in the mining tunnels of Janus VI. The being is apparently destroying machinery and killing the miners, and has the ability to burrow through solid rock.
Errand of Mercy (Mar. 23, 1967): The Federation and the Klingon Empire teeter on the brink of war as Kirk investigates a humble planet caught in the middle—Organia, inhabited by pacifists.
The City on the Edge of Forever (Apr. 6, 1967): In orbit around an unexplored planet, the U.S.S. Enterprise is on red alert as it passes through violent time distortions surrounding the planet. Thus begins what is arguably the best episode of Star Trek ever produced.
Operation: Annihilate! (Apr. 13, 1967): Arriving at the planet Deneva, home of Kirk's only brother Sam and his family, the U.S.S. Enterprise picks up a transmission from a Denevan pilot who has steered his craft into the sun to destroy some unknown menace. Despite some flaws, this is still an excellent episode.
The Doomsday Machine (Oct. 20, 1967): Sent to investigate the destruction of several planetary systems, the U.S.S. Enterprise discovers a crippled starship, the U.S.S. Constellation, floating in space.
Metamorphosis (Nov. 10, 1967): While returning to the Enterprise aboard the shuttlecraft, Kirk, Spock, McCoy and a seriously ill Federation diplomat find themselves kidnapped by an energized cloud.
Assignment: Earth (Mar. 29, 1968): Kirk must decide whether to thwart or help a traveller from the future sent back to 1960s Earth on a secret mission.
For the World is Hollow and I Have Touched the Sky (Nov. 8, 1968): The Enterprise must deflect an asteroid on a collision course with an inhabited planet, but discover the asteroid is a spaceship with a population unaware of the true nature of their world.
The Tholian Web (Nov. 15, 1968): The U.S.S. Enterprise arrives in an uncharted area of space to answer a distress call from the U.S.S. Defiant. The starship is visible on their viewscreen, but it does not register on sensors.
Plato's Stepchildren (Nov. 22, 1968): Summoned by an urgent request for medical help, the Enterprise crew finds a group of aliens who supposedly model their society on the teachings of Plato. Their leader is suffering from a massive infection in his leg and is close to death.
The Empath (Dec. 6, 1968): On a doomed planet, Kirk, Spock and McCoy become the subjects of an alien experiment whose mysterious intention involves a beautiful, empathic woman.
Elaan of Troyius (Dec. 20, 1968): The Enterprise must escort an alien princess to her arranged marriage to seal an interplanetary alliance, but this reluctant bride is no lady.
The Mark of Gideon (Jan. 17, 1969): Kirk beams down to the planet Gideon and appears to find himself trapped on a deserted Enterprise. Spock on the real Enterprise must use his diplomatic skills to deal with the uncooperative inhabitants of Gideon to try to find the Captain. There are plot holes you could fly a starship through, but it is an interesting episode, nonetheless. My take is that no matter how technologically advanced a civilization is, religion can lead them to do some pretty irrational things.
Requiem for Methuselah (Feb. 14, 1969): While seeking a cure for a fever ravaging the Enterprise, Kirk and Spock encounter Flint, a hermit-like Earthman, and his beautiful young ward, Rayna. Spock is really wonderful in this episode.
All Our Yesterdays (Mar. 14, 1969): The U.S.S. Enterprise arrives at Sarpeidon, a planet whose sun is about to go nova. Upon beaming to the surface, Kirk, Spock, and McCoy discover everyone is gone save for Mr. Atoz, the caretaker of a library containing the planet's accumulated knowledge.
Turnabout Intruder (Jun. 3, 1969): The Enterprise answers a distress call from an archaeological expedition on Camus II and a landing party beams down. Captain Kirk finds that Janice Lester, whom he knows, is gravely ill, and Doctor Arthur Coleman is tending to her. The final episode of Star Trek, aired just a month before the Apollo 11 moon landing.

Honorable Mention: The fifth episode of the first season, "The Enemy Within" would have made the list above were it not for Spock's totally inappropriate (and, I'll add, out of character) comment to Yeoman Rand at the end.