The deaths of Switch, Apoc and Dozer in the first movie, especially given how senseless the former two feel.
Switch: Not like this. Not like this.
World Record, one of the Animatrix shorts, doubles as both a Tear Jerker and Crowning Moment Of Awesome. At the end, Dan Davis is left crippled having broken his own 100m record and temporarily escaped the matrix through sheer willpower. As he's being pushed in a wheelchair by a nurse he starts mumbling "free" and stands up, snapping his metal leg-braces in the process, again all through sheer willpower. As an observing agent starts to tell him to sit down he begins to levitate before finally dropping to the floor, all to a soaring, heartrending score. See for yourself.
Neo's Heroic Sacrifice in order to stop Smith's madness from destroying both the Matrix and the real world, and to finally bring peace between the humans and the machines. The last shot we see of him is his dead body being carried away by the machines in a respectful manner, while sad music is being played in the background.
The aforementioned sad music that plays while this all goes down can make you cry by itself without the slightest bit of context.