For science fiction and fantasy...
The Thing (both the 1951 and 1982 versions)
Them!
Godzilla (1954 version with subtitles, although the American 1956 version is also a lot of fun)
Forbidden Planet
The Giant Claw <-- a "classic" of bad movies...seriously, you have to see this
Captain Kronos - Vampire Hunter <-- an excellent vampire film...it's also a mystery...WHO is the vampire!?
2001
Alien
Predator (terrific example of an 80s action movie that is also sci-fi)
Princess Mononoke
My Neighbor Totoro
Shin Godzilla
I love this topic. I may post more later.