Something worth adding, is that "emotional" does not just mean "sad". We have other emotions to consider. One thing I remember from "Titanic" is from the "Nearer My God to Thee" sequence... the band starts playing, then we see the Strauss's, lying together in their bed as water gushes in around them, and I feel my eyes starring to moisten... then I see that third-class mom with her two kids, who wasn't able to escape. And at that moment, at my "Inside Out" console, Sadness mutters "oh, crap" and hurriedly leaps aside as Anger, flames roaring from his head, takes over.
Some Trek scenes that left me positively fuming include...
"The Outcast" - The smug, supercilous, "we just want to help you" attitude of those

-ing government officials as they force Riker's love-interest (don't remember her name) to take the brainwashing treatment. And her "it's Ok, I was wrong, I love Big Brother now," attitude afterward.
"Repentance" - Iko is subjected to "justice" that is effectively no different from the savage ministrations of a lynch mob. And sadly, the Voyager crew just wrings their hands in a "we can't do anything, prime directive and all" sort of way.
And finally...
"Half a Life" - Timcin is guilt-tripped into participating in his planet-wide genocide because his bizarrely hairstyled daughter wants his corpse to rot in a certain spot. In a world containing "Threshold", "Spock's Brain", and "Profit and Lace"... I still regard this as the
worst episode of Trek.
Going to stop before I start throwing things...