Mass Effect 3 had some moments. They were sad, but not really tear-inducing.
Persona 4 had a few moments of sadness, but quite honestly, the Heaven level really was the hardest I had to keep myself from bawling. The music, and the implications presented (stated directly, really, but I won't blame them for that) really managed to get to me. Only level I ran through at full speed, just trying to get to the top faster.
Persona 3 on the other hand is even worse (or better, I guess) in the sad-stuff-happening-over-and-over department due mostly to its darker tone. Though I loved 4, it's 3 that I consider the better game. Wouldn't want to spoil, but the ending to The Journey is both sad and triumphant.
Bioshock Infinite somehow managed to not actually get me to drop (or even hold back, really) a single tear despite my feeling I probably should have. By the end I had already figured out most of "what" was happening and was just waiting for the game to get to the "how" of it all. I admit however: the asylum part was piercing, but didn't evoke sadness; rather I was just speeding through it to get to the inevitable conclusion. I'll credit that to Elizabeth actually being a likable character. The voxophones spread around that level did hurt a lot, though.
Chrono Trigger had a lot of dark/sad moments, but Schala and Magus were pretty tragic, not to mention Frog and even Robo. And then there was that whole Crono thing, and Lucca's solo dive into the past. Hell even the death of the freaking dinosaurs was sad as hell. For a game that starts all happy, sunshine, rainbows and fun at the fairground, it really turns around in a heartbeat.
Planescape: Torment really has a lot of these moments. But then again, it's Planescape; it's amazing, no need to elaborate.
Mother 3 takes the cake though, having a fun opening with a visit to grandpa's house, then a thrilling fire in the woods, and then the game dials up the pain, sadness, heartbreak and sadness to eleventy. Did I mention it's sad?
The absolute hardest parts are the middle of chapter one, with Flint's reaction to the reveal - that by that point had already become pretty obvious, but was still hanging there (and honestly, the way it's delivered sucker punches you DESPITE knowing it was coming) - the entirety of the extremely short chapter six, and the ending "boss" battle(s), depending on whether you played Earthbound or not. The last battle especially can be seen as the epitome of what good storytellers can do: no 3D, no volumetric fog, no HD textures, no lightning effects and no dynamic shadows. Hell, with the game being on the Gameboy Advance, you couldn't even make out the faces on those 2D sprites! But all the emotions were there; full color, eye-gougingly, tear-jerkingly, heart-rendingly there. Then the ending screen... Damned good game.