For me, I was always interested in the character of Severus Snape. I knew there was something, just, 'more', to him. There was a backstory there. I wanted to know why he was the way he was from the beginning of reading the stories.
It wasn't until Alan Rickman became the role that I began nurturing this passion for the character of Severus Snape. (Can I just mention that 'Voice' of his....Oh my.)

So, the question is, is there anything from the books compared to the movies, that just stands out in your mind as something only Alan Rickman brought to the role that wasn't written in the books.
Or something, that was written in the books that Alan Rickman didn't portray that evolved this character into being the sex symbol, dark hero that he has become today?