My favorite will always be Creature from the Black Lagoon (1954).
It's underwater scenes were revolutionary, and I do love the fact that the Creature was designed by a lady (Millicent Patrick), although she was deliberately pushed from the limelight in favor of Bud Westmore, the film's makeup artist. I am always a sucker for grotesque but misunderstood monsters pining after love, haha.
As a few have already said, Psycho (1960)! I loved Anthony Perkins's performance; the ending is absolutely chilling!
I also adore Bride of Frankenstein (1935). The bit with the blind man gets me choked up every time. :<
Speaking of Frankenstein, I really enjoyed Abbott and Costello Meet Frankenstein (1948). Corny humor and monsters--my kind of thing!
The Wolfman (1941) is dear to me, as well. Again with the misunderstood beasts, haha.
And even though it was VERY slow paced and a bit of a bore at times, for Lon Chaney's performance and makeup, I did enjoy The Phantom of the Opera (1925).
I know I've seen plenty good non-horror classic movies, but I can't recall any of them at the moment!