The story as a whole. The fansub literally warns you at the end of 10 that the rest of the series is going to be nothing but flowing tears.
Even the opening can be a Tear Jerker after watching a few episodes, especially if you understand the French phrases.
But specially when Chise and Shuuji have sex in the manga. Some few parts skirt the line with Narm specially when Chise pets Shuji's cock and refers to it as "poor little thing" since he can't make her come, but overall... GAH. ;-;
This needs reiteration. Basically, imagine 13 episodes of Grave of the Fireflies crossed with Gunslinger Girl, then increase the scale and scope. The anime removed the rape because that would've been too depressing.
This AMV, set to Tori Amos' "Winter" (which is a sad song in itself), exemplifies just how gut-wrenching and tear-inducing Saikano is.