As others have mentioned, When Lucien killed my beloved Fairfax, I named the dog after the castle, as a reminder of my ambition to make it my own one day as well as a reminder of where I came from and the hardships I went through, I tried to make the character into me, and i managed it to some affect, so when I was informed that he needlessly gunned down my family and then shot my dog in front of me... Well I wasn't gonna stand for it. I shot him in the dick.
Then of course again, like someone else mentioned, The endings of both MGS3 and MGS4.
3 - When he salutes the tombstone and that single, pained tear rolls down his cheek and you can see the hurt in his eyes, amazing detail for a PS2 game.
4 - For when Otacon talks about how Snake deserves his rest, fucking heart-wrenching.
Another one that really tugged at my heart strings and overall really surprised me was the "death" of Agro, the horse from SotC.
throughout the entire game I couldn't stand how grossly imcompetent it was, It never followed orders half the time, It was constantly a hassle to get onto him in a hurry but when he fell off that collapsing bridge... I wanted me some revenge, Sure it wasn't necessarily the 16th collossus' fault but he was closest at that time, so when I found him I ran at him actually screaming "FOR AGRO!" and then I was flung off the mountain/tower thing because I didn't realise it'd have HAND LASERS.