Can't believe nobody has mentioned Gambling Apocalypse Kaiji or Ultimate Survivor Kaiji or Legend of Mahjong: Akagi
-Two great shows which probably take Best Psychological Anime spot.
I back up those who said Fist of the North Star, Ghost in the Shell, Gurren Lagann.
If your friend ever gets further into anime, tell him to check out Neon Genesis Evangelion, Rahxephon or Dennou Coil.
Also no idea why nobody has mentioned Akira, Spirited Away or Planetes.