Disco Elysium is a fantastic one. There are an insane amount of choices that shape how you go about the investigation of the hanged man and ultimately what happens beyond that investigation. Choices of who to side with, how to side (openly or playing multiple sides, etc.), choices that ultimately define what kind of detective you are (by-the-book boring, superstar douchebag, violent tough guy, Sherlock Holmes-esque genius, etc., including my favorite: Twin Peaks Lynchian detective that bases their decisions off of dreams, intuition and imaginary conversations with the dead body), and even how failing or succeeding at something can lead to progress in very different ways. If you fail to hit that person you tried to punch, or miss that shot with your gun, or utterly fail to convince someone to help you, you progress through in very different ways so that failing your way to the truth is just as satisfying and entertaining as succeeding your checks to get there.

And of course Fallout: New Vegas. Whether you choose to support the New California Republic, Caesar's Legion, Mr. House, or a truly independent New Vegas, none of them are perfect. Each succeeds in an ideal society in some ways but completely fails at others, leaving you to decide which imperfect system you feel is the right one for the world instead of shoving an obvious answer in your face.

The 3 series is the best at this.

The first game in the series is Mass Effect 3, which is followed by Witcher 3 and the sequel to that is Baldur's Gate 3.

If you like randomly made stories, you can try Rimworld.

You will quickly find yourself asking very difficult questions. Is taking on the cripple something you can afford to do? Is using medicine on a less valuable colonist smart? Do you let some of your colonists starve, or start a war with friendly neighbors? Cannibalism will make your neighbors hate you and some of your colonists might rebel over it, but that's better than some of them starving... right?

Disco elysium. Made me want to start it all over again several times.

I'm wildly surprised that no one has suggested "Papers, Please" yet.

This War of Mine. Honestly can't believe nobody else has mentioned it.

You play as a group of civilians in a war torn country. By day you craft things needed for survival like a stove for cooking, guns for protection, barricades to prevent raiders. At night you send one person with a backpack to scavenge an area of your choice for things like food, medicine, supplies etc. The others will either sleep or guard the property. Things you do while scavenging have real effects on your characters. Decided to rob an elderly couple? Your characters will react based on their personality.

Things become grim fast if you decide to start robbing supplies or get attacked. Your players get sick, become depressed, starve, get hurt etc. I've never made it to the end.

It's a great way to understand the struggles of being a civilian in a war. The Polish government actually recommends it for educational purposes and the devs have donated a lot of proceeds to charities serving people impacted by war, including Ukraine most recently.

The obvious answer is Pathologic. You play as one of three possible characters in a black plague-infested town in the russian steppe, trying to help people and survive.

As days go by, the situation worsens and, in order to survive, you are forced to make very hard decisions. Can you spare the food for the others? Will you rob someone of their medicines? Will you risk going to the most dangerous parts of the city, where the stench of infection permeates the air?

I'll quote The Nocturnal Rambler's review of the game, which is one of my favourite video game reviewers:

Making it to the end of a day is a genuine accomplishment in this game, considering all the work you have to do to stay alive, and that the game really doesn't care if you live or die. It won't hold your hand to make sure you get through to the end; it's entirely possible to make it through 10 days and then back yourself into a corner where you have absolutely no hope of survival, short of loading a save from a few (in-game) days ago. Or perhaps to save yourself the agony of replaying several hours of the game, you end up in terrifying, desperate scenarios where you have to sell your only weapon for a few scraps of bread, or murder a child for the medicine he's carrying while you're about to die from infection. That's true horror right there.

It's not an easy game and it's not a good game, even. It's old and dated and janky, but it's also full of charm and personality. I wouldn't say it's a game meant to be played, as much as it is an experience worth going through. You won't have fun playing the game. Even if you can overlook its pain points, it's an objectively oppressive game that will make you feel miserable from beginning to end, and increasingly so. I wouldn't say it's for everyone, and I don't mean that in an elitist way. Some people simply won't stand this much bleakness during the time they are supposedly spending to find entertainment.

I’m a big fan of Tyranny by Obsidian Entertainment. Classic CRPG, isomorphic for the majority of it. The game starts with you making decisions that set the initial state of the world as you lead the army that finishes your evil overlord’s conquest of the world. Then the game truly starts and goes on to be one of my favourite CRPGs of all time.

Pokémon. You get to choose from Charmander, Bulbasaur, and Squirtle for your starter. And everyone you know will judge you for which starter you picked.

Spec Ops: The Line is a pretty decent pick when it comes to having "morally ambiguous choices". the game itself states that there are no "real good choices" and thus, you must pick between the two evils.

Baldur's Gate 3! The amount of ways the game can play out is extremely impressive. There are a lot of tough choices to make that can greatly affect your party and even the world as a whole

Frostpunk

Life is strange is very close to what you're asking, in the game you can rewind time to a limited degree to try different thing, but sometimes your actions only have consequences much further into the game. Even the things that you can rewind and try different things there's rarely a clear better choice, since all of them are morally ambiguous, do you take a picture of the security guard harassing a student or do you intervene? One is obviously better, but the other gives you proof which you might need later on.

Every game on Steam that uses the publisher's launcher.

I'd recommend Tyranny. Its a CRPG, where you play as an envoy of basically villains that are sweeping through the world, conquering almost everything. Most of the choices are pretty difficult, because from what I remember its usually "bad or different bad", without it being clear what's going to be worse. Because you're an envoy for a dictator with the power to literally wipe an entire continent with a single sentence, you can't just go " fuck this, I'm gonna ignore the orders and do good", and balancing the long term and short term consequences makes every decision pretty difficult.

For example, if you get an order to "capture this fortress within few days or I'll wipe the entire island", any small war-crime now may be the long term good option, if it helps you capture it in time, and helping the soldier asking you to help find his wife nearby may be lost time you can't be sure you can afford.

Cyberpunk, and specifically the Phantom Liberty DLC.

I know 2077 has a bad rep for its terrible release, but the game excels in storytelling and mocap above all else. The DLC is accessible at the end of the prologue and requires that you make several hard choices which have a major impact on the dlc's conclusion.

The DLC is also chok full of side quests and contracts that don't affect the overall story but can affect your relationship with various factions, and that are affected by other choices made outside the DLC. The quests also feature various difficult choices. Do you kill the guy you were hired to kill, or do you give them a second chance so they can get treated for the cyberpsychosis that made them lash out in the first place?

I can't recommend this game enough, honestly.

Edit: If you want more details, or have questions, just ask. I don't want to spoil too much.

If you want more cinematic games, the Quantic Dream portfolio has a couple. Heavy Rain and Detroit: Become Human are both notable examples. I remember having some serious anxiety playing Heavy Rain, in the best way.

The X-COM series is pretty much these choices all the time, though less in a moral sense and more a strategic risk and reward sense. What do you use your limited time and resources on, how much do you risk when the stakes are high, etc. It’s a little different than the sorts of decisions you’re thinking of, but quite interesting.

The Walking Dead by Telltale.

Fallout New Vegas. You get it up and running with the GOG and some decent mods you'll have a great time.

Mass Effect 3.

Choosing between the 3 primary colors was the toughest choice of my life.

Minesweeper and a bit of LARP.

Baldur's Gate 3 has a lot of really hard hitting decisions, and I'm in awe at how they're able to make the story work with just how many choices there are.

Life is Strange (any of them, favorites are the 1st and True Colors. Both could be played without the other (separate stories)).

Mass Effect (I started with 2nd) is among the best imo.

Detroit Become Human

Heavy Rain - this one had my first immersed quick decision that I was like, "holy shit I just did that" and it made me question if I would've acted that way in real life given the scenario.

• Detroit: Become Human has some pretty tough decision trees. Not just in how you have to find the options, but even when you only have a few, it's difficult to choose one because none of them are wrong (or right, for that matter).

• Papers, Please seems incredibly easy, but then you're given a choice like "this person doesn't have a permit but their husband did and they say they will be killed if they have to go back; do you do your job or do you take pity on them?"

• Jeopardy. The newest one I know of is multiple choice and some of the answers are hard.

• MGS5? It's not a choice, but damn do I have to take pause every time I get to the part where you have to put down your entire army while they stand saluting you because they're infected by vocal chord zombie parasites. You never even talked to these people to get to know them and it's still like "fuck man these are my friends..."

Fallout: New Vegas. Hell, Fallout 2. In 2 early on, you only have time to one of two quests and people die when you can't help them. You can't save everyone.

Very different from later games where time doesn't matter and the whole world waits for you.

Fallout New Vegas - You can literally help a gang take over the starting town like 5 minutes into the game.

Souls games - The games constantly autosave in the background and (sometimes out of nowhere) present you with some very unclear choices. In Sekiro you have a choice around two thirds into the game which causes the game to end immediately (with a very bad ending); since the game autosaves all the time, once you make that choice you have to start the entire game over and get to that point again to make a different choice.

Most CRPGs I played had meaningful choices (sometimes having extreme effects on the game world):

Planescape: Torment - Best CRPG ever IMO.

Tyranny, Pillars of Eternity - Modern CRPGs by Obsidian, both amazing. I haven't played Pillars of Eternity 2 yet.

A good chunk of comments have spoilers, so if you read this first beware. I guess people like to brag about game knowledge more than they like having other people experiencing stuff.

Detroit: Become Human generally has big overarching choices that are more obviously good vs bad, or rather pacifist vs violent and deviant vs machine, but a lot of the smaller in-between choices can make a big difference regarding who lives and who dies, and a lot of them aren't obvious, especially in Kara's story line. One in particular that I remember can seem like an obvious "doing the right thing" choice but it actually is a choice that can get several characters killed as a result if you do what seems like the "good person" thing. Getting to the end with everyone still alive can be surprisingly difficult without a guide, and there are a lot of different endings and branching paths depending on a lot of different choices. One character has I think somewhere around 26 separate chances of dying in the story at different points in the game. There's an achievement for getting all of them lol.

Heavy rain is similar to DBH but less obvious about having particular good or bad routes iirc. Like it doesn't do the "pacifist vs violent" or "deviant vs machine" style choices, but there are a lot of different choices that can affect the ending and who survives to the end.

Dragon Age Origins is an oldie but a goody with a ton of endings and decisions that aren't strictly good or bad. The following DA games are good too but the first one fits what you're looking for the most.

Those are ones I can think of off the top of my head.

If you use Steam you can search on the category "Choices Matter" FYI

Frostpunk. That game gave me anxiety with the tough choices sometimes.

Deus Ex? The original one

Pyre. The long-term goal is to get you and your boys out of fantasy australia, but there are complications along the way. Namely, who gets their freedom, and who doesn't? Are you really going to let your goofy dog buddy go when he's your best party member? Will you throw the match and let one of your favorite rivals win their freedom instead? Wouldnt it be really funny to let the little goblin loose back in civilization instead of someone who actually wants to go back home to their families? These are the tough questions Pyre asks of you, and they go places.

Prey.

Pathologic 2 - Stress Simulator, decide what to do with dwindling resources. Notoriously difficult.

Orwell: Keeping an Eye On You - The information you pass on, is going to really affect the story. A couple of times, I really felt conflicted about the decision.

This War of Mine - Do you rob innocent at the cost of your humanity or fight those bandits who are looting at the cost of your life

My favorite of all time for exactly this is Spec Ops: The Line. Its a third person shooter and really fun, but its main selling point is making super tough morally gray decisions. Still one of my favorite game stories ever. You can usually get it really cheap and its just perfect for what tou described.

LISA, definitely.

Is Terry’s life worth it?

This time?

New Vegas fits this bill, even quests with "happy" endings leave a sour taste in your mouth, or you putting everyone equally in a shitty situation because you abstained from choosing who to favor. Outer Worlds from the same devs has some quests like this, but the main quest itself is very obviously good people vs evil mega corp.

Wasteland 3 without looking up any guides poses some difficult choices, usually in the form of being forced to side with a certain faction at the expense of another, with no option to skip the choice once it’s presented.

My wife tells me that Rogue Trader has a lot of difficult and unclear decisions like this.