Not mentioned in the obituary linked above (and, I suspect, in most others) is Hurt's role as "Aragorn" in the 1978 animated film version of The Lord of the Rings. That was a film that, when I saw it as a wee lad at a repertory cinema in London (Ontario), awakened in me a lifelong love of fantasy. (I recognize now that that version has many flaws, but when I was a child it was simply magical.) Hurt's voice acting for Aragorn was perfect for the character.
The film version of 1984 also had a profound impact on me. (I saw it before I read the original Orwell novel.) I couldn't get it out of my mind for weeks afterwards, and read the novel and Animal Farm shortly afterwards. Both books greatly shaped my life as well (though obviously in very different ways than the LotR movie).
The Elephant Man, which I also saw as a teenager, had a similar affect on me. It moved me to tears and I thought about it for a longtime afterwards. I think it made me try to be a better person. Few films have that kind of power.
(And of course Alien is one of the greatest science-fiction/horror films of all time...)