What, no mention of Planescape Torment? For shame people. What other game can you make someone disappear by creating a logical argument that makes them believe they don't exist?
Edit: (And in the time it took me to post the wall of text, someone did mention it.

)
Seriously though, while it will be difficult to track down a copy and get it to work on XP, it's well worth the effort. The setting is amazingly developed and is quite far removed from classic dungeon crawlers. There's a breadth of philosophical factions in games and many NPCs have their own set of motivations, logic and beliefs which they subscribe to. The best outcomes for quests come from non-violent and intelligent solutions.
Star Wars: Knights of the Old Republic 2 is in similar vain (the lead writer and director also made Planescape Torment) save it deals with exploring the lightside and darkside and doing a bit of deconstruction. Only problem is that the game is buggy which can be off-putting and is somewhat incomplete. Still, worth a look if you're into Star Wars. Or you could just read the Let's Play guide.
http://fromearth.net/LetsPlay/KOTOR%202/index.html
Deus Ex has a great cyberpunk plot and lots of details which will reward those who like to explore and read everything. Also good for conspiracy theories.
As for anime, well, I guess it depends on how far along the spectrum you want to go. Like others have said, Ghost in the Shell is a very good choice. Look up Seinen anime, which is the sort of serious anime subset you seem to be wanting. Kara No Kyokai is another I recommend. Very good, very moody supernatural anime.