It depends on the vn;
Fate stay night did nothing to me except leaving me astounded about how many hours I've put into it ('bout a 100,), not saying I didn't liked it though. Damn... some of that stuff was intense.
Games like Little Busters! and G-Senjou no Maou have left a HUGE impact on me though. Little Busters kept me on the verge of crying almost throughout whole refrain and I've never had such a strange emotional connection to fictive characters. Right now, even in real-life I sometimes think "It's a shame Masato ain't here, he would've liked this." or "I wonder what Kyousuke would do in a situation like this." I'm never forgetting Little Busters... ever, and i'm really excited for Ecstasy
The reason why G-Senjou no Maou left such an impact on me is because of the nature of vn's; YOU are the protag, YOU talk to all the characters, YOU make the choices etc. I ended up really taking a liking to Haru and the ending made me feel... lost. It was such injustice I thought, and then
I just cracked. In fact, I cracked so bad, that when I was talking about it with my mother, I started crying again. Just recalling the scenes, the dialogue, the injustice was enough to make me cry again. Especially because it all involved Haru.
Anyway, those are the only 2 that had such an extreme impact on me. The rest... not so much. I remember when playing Sharin no Kuni my emotions were also running rampant, yet it wasn't quite as memorable as Little Busters or G-Senjou. I guess that's because of it's good ending and it's pretty straightforward throughout the game.