Someone put all of the major Snape segments of the HP movies in chronological order:
Which causes us to return to the big question: Snape bad? Snape good? On the whole, I think Snape was a bad person who had one soft spot, as he did buy into the Mudblood stuff when he was young, making friend with awful Slytherin people, causing Lily to be alienated. She proved to be an excellent judge of character. Yes, Snape was a good double/triple agent for Dumbledore because of his remorse, but he was still mostly an awful person. His jealousy/bitterness towards James infected everything ever since, including being on the wrong side of the Sirius story in Prisoner of Azkaban.
Of course, Snape redeemed himself by sacrificing everything for the ghost of Lily, but he was not a good person otherwise. Alan Rickman did a fantastic job, of course, capturing the complexity of the character. And the character gave me one of my favorite lines at the start of Intro to IR: that a professor who spent a year in the Pentagon would teach Intro to IR is like Snape teaching Defense Against the Dark Arts.