Anomaly Warzone Earth and Anomaly 2. I've always been a fan of tower defense. What makes these games cool is that it reverses the role. You have to build a squadron and change tactics on the fly to get past the enemy towers.
Anything by Zeboyd Games. Class JRPG goodness with modern improvements. I particularly recommend Cthulhu Saves the world and Cosmic Star Heroine.
Darksiders. These are among the faves of my faves. Zelda-esque dungeons coupled with spectacular combat a really cool story (when you can find it). Each game has its own spin on the formula and those spins contain both my pros and cons for each entry.
Dust: An Elysian Tail. An excellent side-scrolling platformer/hack'n'slash. IIRC, the whole game was made by one person (outside of music and voice acting). Good fun, good humor, good story.
Game Dev Tycoon. I like the idea of making video games. While I will likely never do that, this let's me fulfill that fantasy.
Shadow of Mordor. Before the newer Shadow of War came out with its egregious monetization methods, the original was much better than the LotR-skinned Arkham Clone some would purport it to be.
Prey. Excellent edition to the Immersive Sim genre. The Mooncrash update is amazing.
KOTOR. My introduction to the world of RPGs and still possibly my favorite one that I've ever played. I redefined what I understood a video game to be and opened my eyes to the story-telling capabilities of the medium.
Republic Commando. A poor description of this game would be "single-player Star Wars Left 4 Dead with contextual, tactical commands". While not necessarily inaccurate, this game is much more than the sum of its parts.
XCOM 2. I'm a huge fan of XCOM: Enemy Unknown/Enemy Within. The newest installment improves on just about every single aspect the original had. I get sucked into the game so easily, always wanting to play just a little bit longer so I can finally unlock that next piece of awesome gear.
Now, onto multiplayer...
Atlas Reactor. While I don't play it much, I always come back to this little free-to-play gem. It's like a mixture of XCOM and the "Hero" trope genre (Overwatch, Dota, etc.)
Awesomenauts. I delve back into this one from time to time. It's a side-scrolling platformer MOBA. So, kinda Smash Bros meets Dota.
Cook, Serve, Delicious! 2!! While I could easily put this in the single-player chunk, it does have 2 player local co-op. This fast-fingered game of slamming out food orders and managing a restaurant never bores me. It has some hilarious writing too, if you pay attention to the details.
Divinity Original Sin 1 and 2. Pretty much the gold standard for a CRPG and one I always enjoy playing on the couch with my bro.
Dungeon Defenders. Third-person, hack and slash, tower-defense, loot-em-up, RPG. This amalgamation of genres is one I have spent many, many hours playing online with friends. The sequel is free-to-play and I'd like to pick it up again sometime.
Jackbox Party Pack 3. I always pull this one out when I have a party with friends. The games are easy to learn, accommodate a higher player count, and often result in fits of laughter.
Madballs in...Babo: Invasion. Anyone who has participated in my annual birthday game night already knows why this roll-around third-person shooter is a classic favorite of mine.
Overcooked. Another restaurant game, this 4-player chaotic madhouse of trying to fulfill orders under increasingly ridiculous scenarios is a hilarious blast to play.
Section 8: Prejudice. A shout-out to a game I don't really play anymore, but one that died far too young. This game was destined to be the "Halo-killer". A sci-fi FPS with added layers of customization and tactical choices. I never grew tired of dropping from orbit to anywhere I wanted onto the battlefield, saving up my cash to call down deployables or vehicles, and experimenting with different weapon and mod loadouts. One of my top go-tos was geared to drop right through enemy anti-air defenses, barely surviving. I'd then pop down a signal jammer to avoid detection until my rocket launcher and mortars crunched the enemy AA and, if nobody responded in time, their other turrets and deployables. Unfortunately, the game was plagued by poor decisions that split the small playerbase, required GFWL to run, and eventually the developer/publisher was sued for copyright infringement or something and went bankrupt.
Sonic & All-Stars Racing Transformed. If you're looking for more out of your kart racer than Mario Kart offers, this is the game for you. It's fun, arcadey racing that still requires you to be skillful. There's no cheap-shots like the infamous blue shells either.
HELLDIVERS. From the makers of Magicka comes this tactical top-down shooter. Lots of choice to customize your loadout in this top-down co-op shooter. Of course, everything is going to go sideways when your buddy drops a deployable on your head.
Hidden in Plain Sight. A very simple game for couch-play. It's all about deceiving your friends and making them second guess which of the many tiny dudes on the screen is you while you try to complete one of a few different objectives based on the game mode you select.
Move or Die. Rapid-fire platforming mini-games where you have to continuously run around or you'll, well, die.
I'm going to stop at that before this list becomes truly ridiculous.