The episode devoted to Kepler and Tycho Brahe. "Who Speaks for Earth" qualifies as well, especially the segments where he talks about how humanity has so much potential for advancement and knowledge, yet all too often listens to paranoia or short-sighted greed.
Sagan's description of nuclear war in the same episode is as heart-rending as it is terrifying. Especially the part where he talks about the "additional agonies" that will be suffered by survivors in the aftermath.
A Spacetime Odyssey
Tyson's monologue at the end of the premiere episode of the 2014 series. Anyone who was inspired by a mentor will get teary eyed when he talks about how he knew he wanted to be a scientist, but that day Sagan showed him the kind of person he wanted to be.
He expounds upon that memory in "A Sky Full of Ghosts," where he likens Sagan to one of those very ghosts in the sky, a star whose light still shines long after it's gone.
Tyson's monologue at the end of episode 10, "The Electric Boy" about how the discoveries of Michael Faraday helped transform humanity from a patchwork of scattered, isolated towns, villages, and cities into the globally connected society we are today and how those same forces connect us to the cosmos itself.
The final episode of the season has a Call-Back to Giordano Bruno when Neil talks about the history of science and the importance of free thought—for a few seconds we see Giordano Bruno languishing in his prison cell, before he "escapes" into his dream of the infinite cosmos.
Vavilov: The heroic agricultural scientists starving to death in the Leningrad Siege despite having lots of seeds at their disposal, essentially sacrificing themselves for the sake of a brighter future for mankind.
