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Tear Jerker: Eureka
Stark's final scene with Callister in the Season 1 episode "Right as Raynes". The boy asks him if it's possible to give a computer a soul. Stark replies with tears in his eyes that he knows it is.
In the Season 1 finale, after experiencing the altered timeline where Henry prevented Kim's death via time travel, causing a world-ending paradox, Jack is forced to travel back in time to prevent the interference. This results in a heartbreaking scene where Jack must physically stop Henry from rescuing his wife from certain death, as he screams and cries for him to move.
Nathan's final scene in Season 3's "I Do Over" and it's aftermath. Nobody saw that coming...
The secret behind Eva Thorne/Mary Perkins past, and the men how died in the bunker.
Kim 2.0's death in "Shower the People". Just when it looked like Henry had found happines (again), it's snatched away (again!) in a very cruel way.
When S.A.R.A.H. started to melt (it makes sense in context) and told Carter that it was actually hurting her. The way she said it, in that meek little whimper. That moment really tore at my hear strings.
After spending the episode fighting a dragon, and the reveal that Senator Wen was behind the events of the Season 4 finale, we get a painfully slow execution of Holly, simply for being too smart. Talk about Mood Whiplash...
Fargo's simple lament to Carter after learning he lied to him about Holly's death;
Fargo: You lied to me...
Holly (whose mind is stuck in the matrix), upon realizing that she's dead.
Holly: You...can't pull me out...can you?
Fargo: No...I'm so sorry.
In "I'll Be Seeing You" when Jack finds out Alison died.
Both scenes in "Friendly Fire" where Fargo is going through Holly's stuff. Especially in the second scene when Parrish comforts Fargo by playing D&D with him.
When Andy and Jack are in the jail cell together and Andy reflects back to when he got stuck on titan
Andy:There has to be a moment when you give up hope. When you forget about what's up there, and you focus on what's down here.