It's very rare for games or in fact any media to make me cry. For games the requirements are roughly the same as for books: high literary quality and the right kind of emotional story. However, due to illustrations the immersion tends to be a bit better, so it's not as important that the quality is consistently high. In other words, unlike a book, a visual novel can have this effect on me even if it has some immersion-harming annoyances such as poor grammar.
Even so, the only visual novel that I can remember right now to have made me cry was
My Bully is my Lover.