You must build up attachments to your virtual people before you can start slamming us with emotional moments. Show don't tell is the operative word, and the more fantastical the setting the more human you must make the characters.
THIS
I agree with a lot of the ones mentioned here, including the Half Life series, especially from 2 onward (that includes Portal.) Not just the sad stuff like the end of HL2 Ep 2 (which was gut-wrenching), but also in the action-y moments, and humor. Many of the action set-pieces from 2 onward had great setups. Like when you have to defend this lighthouse, right as you show up, exhausted from a buggy run through ant-lion territory, probably ready for some exploring instead of fighting, a npc who agreed to hide your buggy casually asks you if you'll help them fight against the combine who are fast approaching, and that you joining the battle will make an impact on your sides morale. Then the excellent action music kicks in and combine dropships start showing up. That fight, which would have been just another fight, is now exhilarating, not just because it's well-designed in terms of layout and choreography, but because you have a reason to care about the people involved. They are willing to die for you and what you represent, and they are fighting better because you are with them.
The games are littered with tons of moments like this. The fight in ep 2 with the vorts on your side in the antlion cave is actually rather poorly designed, yet it's one of the best fights in the series, because it makes you 'feel' like you're doing a lot more than you actually are (if you hide in the corner the npc's will kill everyone anyway). The music, dialogue, and timing are perfectly laid out to remind you, again, that you are the hero, and this insurmountable battle is just another 'day in the life' for you. When the npc's shout "THREE RED LIGHTS!" and you start to panic, the music literally changes the emotion entirely from "Oh fuck we're doomed!" to "Fuck yeah bring 'em on!"
For something a bit zanier, the Metal Gear Solid series was really powerful to me personally. The entire game series is all kinds of over-the-top silliness, and is far from perfect, but over time that silliness builds to fondness as it forms a surprisingly self-consistent universe, filled with cheesy dialogue (some of it well-delivered, other parts just...well...cheesy), fourth wall breaking, and impossible phenomenon. For me, each ending was uniquely powerful in its own right, while still managing to top the ending of the previous one.
MGS1 was beautiful in that it effectively tied in an anti-nuclear warfare message directly into Solid Snakes inner struggles, followed by a kick-ass sequel hook with the phone call which would become tradition. It's all very cinematic, but that cinema only means something because you just lived through a hellish experience in Shadow Moses. Snake saw the absolute best and worst humanity had to offer, and saved the world (or at least thought that), and finally found something to live for. Not just a person, but also cause.
The ending of MGS2 did me in for a number. Looking back, MGS2 wasn't really as bad as people seem to remember. While it wasn't steller, it had a unique little charm to it, with most of the problems not stemming from the concept, or the surreal nature of it, but rather that it was rushed. Even then, it took the fact that it was rushed and used it to tell a hell of a story without doing much at all. It took its problems and turned it into its strengths in one of the strongest examples I have ever seen of making lemonade out of lemons. Development time prohibited cutscene creation, an entire bossfight, and many more sequences where you play as Snake. They took that and swung entirely in the opposite direction. So much exposition is designed to literally make you feel uncomfortable. Codec calls interrupt you constantly. There are entire sections of backtracking. Snake gets pulled away from the camera almost every time he's onscreen. You think you are about to throw down with Liquid Ocelot, but no, he jumps off Arsenal Gear and Snake jumps after him, leaving you stuck to fight Solidus, a dude who, while is a bastard and one that Raiden have a personal vendetta with, is not the Big Bad, and his motives actually make some sense. One of people's big reasons for hating it was, of course, Raiden. They wanted to be Snake again so badly that most people missed the point, which was supposed to be a big "take that" to people who want to be like Solid Snake, and that video game characters are shaped by their own merits, not what the player assigns to them. You are not Snake, and you are not Raiden either. You are your own person, and they are their own characters. Unlike all the other MGS games, this one is literally a snapshot of the life of a soldier named Raiden, and his encounters with Solid Snake. He is an observer, one who comes to his own conclusions, as are you to Raiden. It is all symbolized perfectly with the tossing of the dog-tags.
And then the phone call jettisons everything you thought, wrapping up all character development while body-slamming you with a new mystery on top of all the other ones yet to be solved. "What the hell?" indeed.
The third is arguably the most "normal" of the games, in that it sticks its wackiness to keep in line with spy-movie cliches and the plot-twists we've come to expect. Unlike the first two, which ended on a triumphant note, (though 2 was a lot more bittersweet than one, leaving the plot unfulfilled), this one was a hell of a downer ending. Yeah, Snake saved the world, yeah nuclear war averted blah blah blah. Guess what? Boss is dead. You killed her. She didn't do anything to deserve it. Her own country threw her to the dogs and smeared her name as a traitor for the greater good. There is nothing you can do about it to preserve the peace. But at least she was cool with it, right? She was willing to do this for her country. At least you get the gir..oh wait she's a Chinese spy and she took the microfilm with all the money locations with her. The game perfectly laid out Naked Snake's motivations for what he went on to do. Hell, how could he not, after everything he saw and did.
And then there is four. Right from the start, you know this is the end. Its all going down. Snake is dying. All the best laid plans from the previous three games have utterly failed. One last shot at redemption. Snake and co. shut down the Patriots, but him and liquid "still have a score to settle." It's an intense, no-holds-barred fight with two old brothers beating the shit out of each other on top of a giant warship, while constantly dredging up memories of the entire Metal Gear series. After that fight, half of everyone is either dead or so emotionally/physically scarred that a simple wedding holds enough emotional gut-punch. And then Snake has to eat his own gun. Credits roll.
Or not...
Turns out, no. We get an overly long explanation of everything, clarifying all the loose ends, and revealing that Ocelot was actually a 'good guy' all along. Now, this is so dialogue-heavy and long that it almost completely loses the viewer (one of the faults of the series). In my opinion, however, it completely redeems itself with the last few seconds, with the highly-emotional cigar drop and Big Boss's final line, "This is good, isn't it?"
Cue credits, and a promise of Snake to live out the rest of his short life peacefully, and to quit smoking.
This is how you tie a franchise together. The endings, bossfights, and emotional moments in between, are so powerful, IMO, that they make it worth suspending your disbelief and forgiving with Kojima's crazy-ass tendencies, ridiculous-length cutscenes, and general implausibility.
