Two episodes came to mind for this. The first is a Deadlands session I'll be writing up soon, with fear and phobia and great interaction between Solomon, Carson and Tesla. I shan't say too much, except to remind you Solomon's "worst nightmare" is that she's a were-puma and, in that form, slaughters innocent people (this being far away from her pacifistic nature), and that in Deadlands, your worst nightmare, your biggest fear, has a habit of finding you...
The second was a single scene in Aberrant, recounted here (when I was still writing the game in third person). Chrissie's relationship with her parents had never been particularly good: they never showed her much affection, growing up, and she rebelled against their materialism, their plans for her, their lack of interest in her, and this was the first time she'd seen them since her Eruption.
They started out simply ignoring her, but her attempts to talk to her mother ended up with her mother denying their very relationship. It cut my character deeply - I really felt it. The atmosphere in the room was intense as we played the scene.
Afterwards, my GM apologised to me, for being so mean, but I loved it.
What about you? What tricky experience have you had? Mine were emotional, but perhaps you have something more practical. Let me know below!