Well, to be honest, my experience with the cyberpunk genre is really limited to mods and Deus Ex. The mods are for Half-Life2, one is space-related (my Freelancer experience gives me a bit of an edge with Newtonian flight) the other is just pure, hard cyberpunk. Dystopia.
It's a multiplayer game, with three different "classes" of character on two teams. You've got light, medium and heavy. Light characters are hackers, and although they have some nifty abilities in the real world (automated turrets, sniper rifles, disabling enemy stuff) they should really spend most of their time jacked in to cyberspace, where they can jump about and throw viruses at each other, while trying to unlock/lock that door/turret/power core.
Mediums are essentially just your average grunt. Heavies are slow, heavily armored, and get access to the biggest and badassest guns in the game, just like any character with the "heavy" adjective should.
The other one I currently forget the name of, but it's similar in a few aspects. Overall, Dystopia is a bit more polished, but the other game has some really neat weapons and spaceship battles (trying to remember where the hell that damned docking port is can be a pain though... Especially if you happen to be flying the troop shuttle and you've got five guys complaining about thwy they aren't on the other ship yet and could you please avoid those turrets).
I'm unaware of any MMO cyberpunk games, but the ones I listed (aside from Deus Ex) are at least multiplayer. But, as I said, cyberpunk's not really my thing.
There was one game I tried a while back that looked like it had some pretty insane depth, but I can't remember the name of it... It was singleplayer, and I'm not sure what specific style you're looking for as far as how many people are playing. There was also a really wacky problem it had with my computer, where the entire world would just turn dull orange and I couldn't see where I was going. I never fixed it, although I did cheat to see what all the items were that you could get your hands on. Laser flail? Hell yeah.
It was kinda old though, so the graphics weren't that great (by current standards). If only I could remember the damned name of that thing...