These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Crowning Moment of Heartwarming: When Cooper finds out that Charlotte was raped, he sits down with her, tells her he loves her (no matter what), vows to protect her, and ultimately helps her find the strength to identify her rapist. May also be a Tear Jerker for some. It was just that good.
Ensemble Darkhorse: Charlotte, for many fans, once she was defrosted. Probably helps that KaDee Strickland pulls off the whole Southern-Belle Texas-accented charm with perfect ease.
Sheldon and Amelia have a pretty passionate fan base, although Ryan and James don't often get the Die for Our Ship treatment ( although that may be because Ryan did).
"Funny Aneurysm" Moment: Early in Season 3, in order to get some perspective on one of her patients, Violet poses Cooper a hypothetical: Charlotte is raped, falls pregnant by the rapist, and decides to keep it. Cooper responds with "Don't hypothetically rape my girlfriend!". A year later, Charlotte being raped is no longer a hypothetical.
Growing the Beard: Every fan will have a different answer to "When did the show completely step out of the shadow of Grey's Anatomy and become its own entity?", but they can all agree that "Did You Hear What Happened to Charlotte King?" is a contender.
Ship Sinking: Cooper and Violet after he got together with Charlotte and lost his feelings for Violet.
Addison and Pete at the end of Season 3, when they respectively choose Sam and Violet.
Sheldon and Amelia, after she straight-up tells him she'll never love him back during her intervention. While they still got back together, they're more akin to friends than an actual couple. Doesn't help that the latter just went through the death of her boyfriend and son.
The Woobie: They take turns. Actually, there isn't a single character who didn't end up as the woobie at one point or another in the show.
Wangst: Holy shit, where to even start? Let's just say these people make The Winchesters look like a perfectly happy, well-adjusted, picket-fence-rockin' family.