I'm surprised people even know about Paradise Cracked and Cops 2170.

Omikron's an RPG. It's good, too. A little disjointed, but ridiculously ahead of its time. Like one of the other posters said - a number of Adventure/Cyberpunk games, less so on the RPG front. I'll look through my stack when I get home. I have a few of the adventure ones.
Here's what I can think of besides what's been mentioned:
Shadowrun SNES was a solid RPG too if you liked Shadowrun Genesis. The modern levels of Vampire the Masquerade: Redemption had cyberpunk elements that I found mildly reminiscent of Shadowrun, though I wouldn't call it a cyberpunk RPG. Anachronox was modern and quite good, though cyberpunk is debatable. It has noir elements, but stronger affinities for JRPGs style of storytelling than Gibson. Try it, I think you'll like it.

I'd suggest the Phantasy Star RPG series (the fourth was my favourite...), but I wouldn't call it cyberpunk... just futuristic fantasy I suppose. It does involve cloning, genetic engineering, multiple planets and space flight though at various points.

Does Uplink qualify as an RPG?

Calling it cyberpunk is a stretch, but Phantasy Star IV was an awesome JRPG.

Thief: Deadly Shadows while technically NOT an RPG is an RPG since you play the role of the main antagonist/protagonist.

I think "simulation" fits it better.
In any case, it's a great game. Best "hacker" game I know.

I think you might be mixing up cyberpunk with steampunk...

If that does, I'd recommend Hacker Evolution too

Dammit, my bad. =)
Maybe....shit, I don't know if I even have TOUCHED a cyberpunk game in my 15 years of life... Does anyone here consider Half-Life cyberpunk?

Brilliant inclusion. I wouldn't have picked it as Cyberpunk myself, but damn. It just fits. "Suspended" would work here too, I think. As IF goes, these two are sterling examples.
Is this the one with Homer, the storytelling AI? I've been looking for a copy of this one for a long time. *hint hint* Though it's not really a game. More like a slowly revealing book.
Neuromancer is an RPG, I'd say ... It has the leveling up of programs in your deck, and the hacking of ICE feels a lot like trading skill-based blows in an RPG.

Not really. Cyberpunk generally refers to games, movies and books that feature dystopian futures, Cybernetic augmentations and computer-neural interfaces. William Gibson's Neuromancer coined the phrase Cyberpunk but its featured in a lot more media since then. Shadowrun is the most famous pen and paper RPG to be based around the Cyberpunk idea. A lot of the old Shadowrun books were released free on the net after the collapse of FASA so its worth hunting them down.
Some of the books are worth hunting down as well especially 2XS, Burning Bright, Never Deal with a Dragon and the Dragon Heart trilogy.

Half-Life is in a dystopian future.....
But thanks anyway Jesus, even though I reject you. =)

Yes but it doesn't have the other elements. The Matrix features computer-neural interfaces but is not Cyberpunk. Johnny Mnemonic however is very Cyberpunk.

I'd say Matrix is cyberpunk (by way of Japanese anime like Ghost in the Shell, etc which is quite cyberpunk). The problem is it's just not very good, at least after the first one (and excluding the really great Animatrix).
Incidentally, I thought of another group of games. While lacking the typically libertarian cyberpunk leanings and a tad bit closer to mecha than cyberpunk - the Front Mission series is in the ballpark. OP, you might like that if you're sick of fantasy RPGs.
There's also the post-apocalyptic occult cyberpunk of some of the Shin Megami Tensei games (e.g. SMT3 - Nocturne or Soul Hackers). Not all of them are cyberpunk, but some very clearly are. They are very, very different from most JRPGs. speaking of Atlus, Maken X, made by the same team as the SMT series is one of the more interesting cyberpunk games I've seen. It involves brainjacking (think Freejack) and some other very cyberpunk things. FPS for the DC.
Otherwise, as has been mentioned, there's Blood.net and some others.