Anime you say?
When it comes to favorite movies for me it's hand down Ghost in the Shell and Ghost in the Shell: Innocence movies as well cyberpunk being my favorite genre and they where very thought provoking when I was done watching. Honorable mentioning of some other titles of movies I liked a lot would be Jin-Roh, Sword of the Stranger and Wings of Honneamise: Royal Space Force.
As for the Series to name a few of my favorites those would be Ghost in the Shell: Stand Alone Complex 1 & 2, Psycho Pass Season 1, Vision of Escaflowne, Code Geass: lelouch of the rebellion & R2, Fate/Zero, Black Lagoon, Cowboy Bebop, Full Metal Panic, Future Diary and Hellsing Ultimate.
Now ofcourse I have guilty pleasures like the Mind F--k that is Evangelion but also things I ignore they exist like the Ghost in the Shell RISE OVA's, the movie that followed suit after the OVA's and the live action abomination. Now it's fair to note that I haven't bothered watchin the new anime movie of Ghost in the Shell and the live action one as the first well from what I could gather of the OVA's in which the writer turned all characters into a running joke and plot was left to be desired I wanted to prevent further damage done to my holy grail of franchises. The Live action, well knowing Hollywood they would trade in plot for action and not be thought provoking in the slightest so why would I even bother.