I liked Slice of Life anime in my teen years. Now I don't watch many of those but looking in past I remember I got emotional after few:
Angel Beats and ending of 10th episode hit me hard
Clannad didn't hit me as much as I expected. only one episode had make me cry (this one on flower field)
Tasogare Otome X Amnesia - like whole story of Yuko was kind of fuckin sad, last episodes especially,
Great Teacher Onizuka - I cried on last episode cause I realized it was over.
Sakurasou - similar case I liked characters so much that I was sad it ended
Naruto - like most of character had fucked up life especially antags like Itachi, Sasori, Gaara.
But maybe the most memorable scene in anime that give me tears every fuckin time I watch it is...