I had a recent conversation with a successful professional, who had never heard of Montgomery Clift - I was nonplusssed, owing to her apparent high degree of intellect but I also realized that exposure was exposure, so I strongly recommended
A Place In The Sun and
From Here To Eternity
The most interesting thing about his relationship with Elizabeth Taylor, (they were best friends) was that she saved his life:
http://en.wikipedia.org/wiki/Montgomery_Clift#Car_accident
I also told her about one of my favorite Clash songs,
The Right Profile chronicling his tragic post-crash addiction and depression.