So, for a cyberpunk game these days, here are my thoughts:
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My top choice would likely be Stars Without Number with Polychrome and maybe a few other supplements (Darkness Visible comes to mind). It’s basically B/X-flavored D&D passed through a sci-fi filter, and Kevin Crawford has some of the best sandbox game mastery advice around. For anything sci-fi, SWN is my go-to system, especially since there are great supplements for different flavors (military, trader, spies, and so forth).
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@LizardMan has a neat minimalist cyberpunk system that’s worth checking out. It’s not exactly the system I want to play with, but his procedural content generation is top notch, and I respect the purity of his rules approaches.
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If you want to use an actual old school ruleset, Cyberpunk 2020 has some flaws, but the character creation creates a lot of great hooks, and the combat system is detailed in a way that can be fun (check out Noisms thoughts on it here and linked from there). If that doesn’t work for you, the Fuzion rules were R. Talsorian’s attempt to take the best of Cyberpunk 2020 and Champions and produce a generic RPG system. I had a lot of good gaming with the Bubblegum Crisis RPG using the Fuzion system. It’s a D10+attribute+skill system, which is great if you like a nicely systematized ruleset, and BBC was itself a Cyberpunk+Mecha setting.
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The Black Hack Cyber-Hacked is a nice minimalist ruleset with a strong old school flavor.
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I’ve given some thought to running Blades in the Dark as a cyberpunk game, but I haven’t tried it. The mission-based and team-focused structure would work especially well for a Shadowrun style game where the players are a team of mercs that regularly get jobs. That would take some work to convert, though.
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You could always use one of the versions of Shadowrun, but it’s a fairly clunky system with its own challenges (I don’t know the newer editions particularly well). It’s a die pool system, and the die pools can get out of control pretty easily.