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Tear Jerker: The Matrix
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.
Trinity's death in The Matrix: Revolutions.
The deaths of Switch and Apoc in the first movie.
Switch: "Not like this."
Neo's sacrifice in order to stop Smith's madness from destroying both the Matrix and the real world, and to 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.