American McGee's Alice is intentionally weird and disturbing, given that it's basically the warped version of a child's whimsical fantasy. However, the deaths of the Gryphon, and the Cheshire Cat are particularly heart-wrenching, especially since this causes Alice to have her Heroic BSOD after calmly weathering all the other freakishness she's seen. The latter actually caused one of the guys doing a Let's Play of it to state "That was for the Cheshire Cat, by the way." during his thrashing of the Queen of Hearts.
And let's not even get into the fate of the March Hare. At least the Dormouse was so out of it that he barely knew what had happened to him.
For me, it's the opening cinematic that gets me sniffling. Alice's voice actress may not sound particularly like a little girl, but the way she cries out, "Mum? Father?!" just — And then you hear her parents screaming for her to get out, save herself, before there's this awful crashing noise. . . .
It's possible that's the Mad Hatter, the March Hare and the Dormouse screaming for her to get out, since all of the voices sound male. Which still makes it a Tear Jerker, considering they were still in their "right minds" (still mad, but harmlessly so) and obviously cared about Alice... that is, before she crossed over her Despair Event Horizon and turned them into twisted versions of their former selves.