Wow guys that's a lot of great stuff! I'm gonna start adding some of these to my list :P
Being a Kojima fan I must play Snatcher like now :)
I've never played it sadly.

I wanted to recommend Rent a Hero which is a cool slightly unheard of point and click adventure.

Cheers,
Myles Blasonato.

Shadowrun for the Super Nintendo (Genesis game is different) comes closer to being the embodiment of cyberpunk for me than any other game, book, or movie. The music and atmosphere are oustanding...it's gritty and cybery and depressing (all key elements of cyberpunk IMO). It's an "action RPG" so you need to be okay with action, but there are adventure game elements such as lots of dialogue and some minor "puzzles" with figuring out what to do next.