Abzu. Zen exploration game. Not really in any of the genres you mentioned, outside of maybe LOOSELY rpg,  but it's so amazing I can't not mention it. One of the only games I've ever enjoyed enough to write a full review of, can provide full text if desired. Easily one of my favorite games of all time.

Bastion. Amazing uh.. slightly-topdown-shooty-platformy-RPG-y game-thing. Made almost everyone's Game of the Year lists in 2011 when it was released, and has a consistent 9+/10 on every scoring metric ever. I describe it badly, but it's great.

Batman: Arkham Asylum, Arkham City, Arkham Origins. I personally didn't get into them because they're a bit heavier on brawly-combat (and have inspired a whole subgenre of combat in games) and that's not to my own taste, but the series is SUPER well-loved by others.

The Banner Saga. Turn-based strategy, but with heavy RPG story to it. I admit to not having gotten very far in it because I have like 300 games and not nearly enough time in a day, but what I have played was PHENOMENAL.

Brothers: A Tale Of Two Sons. Has won a BAZILLION awards for innovation in combined mechanics with story. RPG. I personally found it overrated, but still a good game, but it's on so many people's "Favorite Games Of All Time" lists that again, can't really avoid mentioning it..

Brutal Legend. Metal-themed RPG. Seriously, that's a thing. Again, haven't played as much of it as I'd like, but from what I played, it was very enjoyable. Maybe less so if you dislike metal.

Chroma Squad. Power Rangers-themed RPG/tactics game. Lots of meta humor, if you've ever been into the genre. If you weren't a fan of any of the shows, don't bother with this one IMO.

Costume Quest. Halloween-based RPG. Probably better to wait until October when, if it's available, it'll inevitably go on sale. Don't bother with the sequel.

Darkest Dungeon. Cthulhu/ancient-eldritch-horror themed Roguelike. (In this case, I mean you have disposable characters, levels/dungeons are procedurally generated, resources are limited, and you're expected to make the best of bad situations.) Absolutely KILLER theme, and while it's maybe a bit creepy for my taste, I can recognize that it's a FANTASTIC game and theme. Very well executed in general.

Divinity: Original Sin. One of the best CRPGs in recent years, though I do recommend playing co-op with a friend. It's a lot more fun with a buddy than alone.

Dragon Age: Origins. A bit dated on graphics, but easily the best Dragon Age game (fantasy RPG). Probably one of my favorite games of all time, tbh.

Forced Showdown. Twinstick, top-down shooter. I know you mentioned not likeing shooters, but since this one is topdown, I think it counts. The theme is what sells it for me -- this entire game is you playing a contestant on a gameshow, and the sense of humor is AMAZING. It's a weird game to describe, though, so if you're interested, I recommend searching for "WTF is Forced Showdown" on youtube and taking a look at TotalBiscuit, The Cynical Brit's video called After Hour: Forced Showdown. He covers it well.

Guild of Dungeoneering. Again, roguelike game in that everything is procedurally generated, you have limited resources, and your characters are disposable. Fantastic, pen and paper D&D-like theme that got me into it, and probably the best menu music of any game ever.

Middle Earth: Shadow of Mordor. Arkham-style combat, which again, I wasn't into, but the entirety of the internet fucking LOVES this game.

Ori and the Blind Forest. Super beautiful RPG/platformer. Really, just gorgeous; I can't begin to describe how pretty this game is. Also has a decent story, though I admit I didn't get very far since I'm HORRIBLE at platformers.

Pillars of Eternity. The single best CRPG since the golden days of old. Seriously, if you liked the old D&D games like Baldur's Gate, and this is available, I pretty much consider it a staple of the genre.

Renowned Explorers: International Society. Turn-based Strategy/Tactics game with RPG story elements and a great sense of humor.

Shadowrun Returns, Shadowrun Dragonfall, or Shadowrun Hong Kong, all by Harebrained Schemes. Great CRPGs based on the Shadowrun universe.

South Park: The Stick of Truth. If you're into South Park's sense of humor, you'll love this. RPG.

The Stanley Parable. Mind-fuck game which I really can't describe. Search youtube for WTF Is/Isn't Stanley Parable.

Thomas Was Alone. Platform-y game about shapes. Yes, about shapes. And yet, those shapes have more life and personality than half the actual people in most video games. Absolutely fantastic narrative to the game, though again; I suck at platformers and didn't make it as far as I would've liked.

Transistor. Made by the same people as Bastion, and a FANTASTIC game with an emotionally-charged soundtrack. Made most people's Game of the Year lists in... 2014, I believe, though it might've been 2015.

Un-Epic. Platformy RPG with geeky references and humor.

The Witched. Not personally my taste, but still great RPGs. The Witcher 3 made just about everyone's "among my top games of all time" lists and is generally treated as the video game incarnation of the second coming of christ.