https:// www.gog.com/en/games?query=cyberpunk&order=asc:title (mind the gap)

VA-11 Hall-A: Cyberpunk Bartender Action
ANNO: Mutationem Community Wishlist
ANNO: Mutationem Steam Demo

I got Remember Me for the PS3 for cheap in a Humble Bundle years ago and was impressed by it, having never heard of it before that.

I wish Capcom would stop holding it hostage.

Damn. I thought it was here. Weird.

I'd also recommend Hard Reset.
It's nothing like Cyberpunk in gameplay, but as this is a linear-arena-shooter*, you may have fun with the combat as an fps with similarities to classic shooters like Quake, Serious Sam, Doom...

*'linear-arena-shooter': Walk forward a bit, explore the map, search for ammo, secrets, etc, reach an open not-always circular area in which many enemies show up, story exposition here and there per level, some levels fight a mini boss or a boss at the end, and so on.

COMBAT:
The focus here is that you start only with 2 guns which you can be upgraded to essentially become 10.
Using them in different ways can give you advantage in combat facing the enemies.
Classic Serious Sam and Modern Doom-like strategies of shoot-change gun-shoot / shotgun-machinegun-rpg-machinegun-shotgun work here well too, albeit enemy reaction is really limited and not always you feel the impact of a good and fast swap-gun gameplay.
You also have a katana. Its useless most of the time. (Except when fighting ai-controlled-zombies).
This game wasn't designed with melee combat in mind, so, if you focus on melee you will probably die fast, depending on what difficulty you choose to play on.

LEVELS and MAP DESIGN:
Levels maps feel well designed with many secrets hard to find. Combat "arenas" of each level, though, sometimes feel too small with tight corridors, making survivability and mobility quite hard. And although linear, this game has some good awe-inspiring vistas and well made scenarios per level. Be it from the ground looking giant buildings in the dark and hard city, be it from the top of a destroyed building never repaired by the AIs looking at the giant digital outdoors, be it from the machinery cemetery where once there was a human factory used by the resistance agaisnt the AI uprising, now dominated by the same AI and used to create robots to their army with rests of dead bodies and destroyed tech. I really enjoyed the scenarios.

ENEMIES:
Talking about enemies, they're repeated way too much, specially in the beginning. But they start to vary later in the game. Bosses are fun in my opinion, mini bosses feel nice to understand and destroy. Their design is based on what I said before about AI using rests of machinery and dead human bodies to create their soldiers and they do give you some scares depending on the level which is also fun if you're into light-horror and some jumpscares.

STORY THEMES:
Story is interesting but not really well presented. It feels that the developers assumed the player already know about the themes explored in the story and never really develop them much more than just throwing them at the player's face. Albeit sometimes you do get more development through in-game conversations from the characters. The central theme of this game is the risks present in transhumanism, the risks of developing AIs without limits, how long can humans really live 'in peace' with such technologies and use them for good, etc. Same themes found in any Future-Cyberpunk themed stories. Most of the time story exposition is done through comic-like cutscenes at the end of each level. I like it. I've seen better art done before, but the art in this game is good enough for me to call it good.

I should also talk about the Sound design, but this text is long enough already. :)

Anyway, it is a good game with some design flaws which can be seem by those nitpickers out there, but fun nonetheless.

Wow, I didn't expect so many responses. Thanks everyone for your suggestions! I'll look at them all. :)

Haven't seen these mentioned yet:

Neon Chrome [standard edition | Deluxe Edition]
JYDGE

Shadowrun (SNES, find the rom and an emulator, I recomend Higan)

Shadowrun Trilogy - available here on GOG.

Beneath a Steel Sky - PnC adventure game, don't know if it qualifies, free on GOG (and everywhere, the devs made it freeware)

Beyond a Steel Sky.

Cyberpunk is a cool game?

Sorry, had to get that one in.

Do you want "Wow Cool Robot" Cyberpunk; the aesthetic, or do you want class warfare, stratas of depth, and the actual themes of Cyberpunk?

[url=https://www.mobygames.com/game/genre:cyberpunk-dark-sci-fi/]Anyways, here's a Mobygames list.[/url]

nvm

Deus Ex, Cyberpunk, and Blade Runner are the big titles/franchises that obviously use the theme. I won't go into detail since many people has mentioned it but obviously check them out.

Dex, VirtuaVerse, and the Shadowrun series have been given away in the past, so if you're a giveaway claimer check them out. I only played VirtuaVerse, it's a good P&C game.

On a related note, Technobabylon is probably my favorite cyberpunk P&C.

Whispers of a Machine is another amazing one.

Transistor is a great isometric combat game that you can play in an almost turn-based combat. The aesthetic and soundtrack are beautiful.

Transient is a pretty interesting mix of cyberpunk and Lovecraftian horror. Interesting unusual concept, but I had fun playing it as well as the Resident Evil/System Shock type minigames.

else Heart.Break() is a game in which I would kindly ask for you to consider.

Due to its exceptional usage of programming, it is a game that I hold so dear. However, even if you have zero experience with programming languages, I believe that the game can still be enjoyed.