My take on the list, with added notes. A few of my picks...I don't know what you've seen and what you haven't, but the short list of anime I generally give people goes something like -
Cowboy Bebop (Space opera) (Unforgiven/Red Dead Redemption in Space but only 1/3rd of the time.)
Ghost in the Shell:Stand Alone Complex (Cyberpunk police) (Existentialism disguised as cop show)
Death Note (first season only, second season is garbage) (Supernatural vs Police) (What is World Peace/Order worth?)
Attack on Titan (Action/End of humanity) (2nd Season is still a bit a ways away so don't expect answers)
Samurai Champloo (Anachronistic historical fiction drama) (Currently airing on Toonami)
Big O (What if Batman was about mechs and animated by the same guys who did Batman: The Animated Series. Yes, really.) (More Existentialism, missing third season that would have explained everything)
If you've seen all that or they don't sound like they appeal to you, you might also try
S-Cry-Ed (Rivalry, Order vs Freedom) (Classic Shonen style with modern production values)
FLCL (Batshit acid trip) (What does growing up mean and who decides when you've done it?)
Paranoia Agent (Supernatural vs Police) (Nature of guilt, want, and denial. Self Destruction)
Trigun (Wild West on a new planet) (What are your morals worth?)
Irresponsible Captain Tyler (Space Comedy) (What do you truly want out of life?)
Armored Trooper: VOTOMs (Real Robot) (Hardest sci-fi of Real Robot genre)