Hmm. The following titles have all provoked what I would call "a strong emotional response" due to elements of great pacing and character or mood plus some memorable moments or levels:
1 - Ico
2 - Shadow of the Colossus
3 - Flower
4 - Cloud
5 - Silent Hill 2
6 - System Shock 1 & 2
7 - Uncharted 2
8 - Valkyria Chronicles
9 - Portal (awesome, awesome use of mood and tone and pacing and cake)
10 - Half Life 2 plus Episodes
11 - Vampire Masquerade : Bloodlines
12 - Siren Blood Curse
13 - Call of Cthulhu Dark Corners of the Earth
14 - Amnesia Dark Descent
15 - Thief 3
16 - Halo CE (the good version on PC - I keed I keed)
Some more recent examples without going back to the days of stuff like Westwood's excellent Blade Runner title.
I like some of the moments/cutscenes in stuff like Final Fantasy / MGS etc but I find I just can't quite connect with their more erratic tone and nature and approach. RPGs in general I always seem to find a mismatch between gameplay style and narrative. It's hard to put my finger on why as they're often loaded with 'big moments' in cutscenes, but they never quite work for me.
Try to be reasonable... its easier than you think...