Early 2000's? Old? For me it's way before then. Tons of film noir from the 40's and 50's. Men with square jaws wearing hats and dames worth killing for. Hitchcock of course was a master of the psychological thrillers. Like Psycho! North by Northwest, The Birds. Many more.
But if it's post 2000 you want. There's some way offbeat psyco-sci-fi films that may interest you. Beyond the Black Rainbow is pretty damn weird and hard to figure what, why and how. And Under the Skin, is very freaky. Slow moving, but bizarre. And a Spanish film called Time Crimes will keep you wondering till the end.