"Die Hard" is definitely my favorite movie in which he appeared; it's still one of the best action movies of all time!
He was also my favorite part about "Robin Hood: Prince of Thieves" -- along with the iconic musical main theme of the movie, which I love too. I don't care for the movie as a whole, but it has a special place with me because it was part of my childhood. And Alan Rickman's portrayal of the evil Sheriff was hilarious and unforgettable. xD
I'm not a big fan of the Harry Potter franchise, though I have seen all the movies, and I really admired his portrayal of the Severus character. From the first movie, he always made you feel -- correctly -- that even though he behaved like a villain, there there was more to him somehow. And indeed there was. His acting in the last movie especially -- when all was revealed about his backstory -- was touching and brilliant.
He was my absolute favorite actor and I am beyond saddened that he is gone. I don't think he got enough credit for his work. My favorite is actually something that is not as well known as the ones you posted here, but I highly recommend it. It is called Snow Cake. Sigourney Weaver is brilliant in it as well... This is one of my favorite clips from the movie:
Sweeney Todd. I really hated hus character in Sweeney Todd but that's a good thing because you were supposed to hate him. I'm so bummed that we'll never get that Alan Ruckman voiced gps "Take the upcoming right, do not dissapoint me. Congratulations you missed, now make a u-turn when you can. Do. Not. Fail. Me. Again.
The deaths of other celebrities didn't bother me much. Robin Williams' death hit hard, but this one is absolutely devastating. He was amazing. Charismatic, talented, versatile, kind, funny... I hate getting older. At some point you just see everyone around you dying.