I have incredibly poor taste, low standards, or both. Here's some recommendations that aren't the mandatory name drops of Shadowrun, Syndicate, and Deus Ex.
I really like the Syndicate FPS they made on 360. People hated it at the time for turning a RTS RPG into a FPS, and for using dubstep in the trailers, but look past that and it stands on it's own (and honestly, I think dubstep fits cyberpunk). The co-op in particular was outstanding. Shame I rarely found anyone to play it with. The single player is ...okay. The sound effects and feel of the weapons was great.
Not really cyberpunk per-se, but Dredd vs Death is really good. It was a budget game if I remember right, but get past some compatibility issues (turn off all overlays helps in my experience), set expectations accordingly, and it's good fun.
Not cyberpunk, but Urban Chaos: Riot Response on PS2 and Xbox nails the bleak grimdark atmosphere mixed with satire tone of the good Robocop movies. Also, you can twat guys with a riot shield.