Harry Potter was one of the greatest novels of all time (according to many) and starring in it has introduced him as an actor to many viewers, whether young or old (as I stress, Harry Potter is not and will never be a children's book)
My answer in short? Always.
As Professor Snape, actor Alan Rickman was absolutely perfect. I think a good acting work should be judge by how successfully a character convinces and is able to "transport" the spectator inside the action, and that is exactly what Rickman achieved in the Harry Potter movies. He will be missed and never forgotten, and he will be best remembered as Snape, for sure.
I believe that Alan Rickman will be best remembered for his role as Professor Snape in the Harry Potter movies because of the massive fans that the Harry Potter books and movies have amassed. He will be remembered by this role especially by the younger generation who most likely have never seen any of his other works.
I'll always remember Alan Rickman as Hans Gruber, the memorable baddie from Die Hard, and his debut film role. But in the public consciousness, he'll be remembered as Severus Snape, as Harry Potter was, perhaps, the most culturally significant achievement in the Millennial era, which is the final generation familiar with Rickman and his work. That said, his role as Snape was excellent, and there are worse roles to be remembered for.
While younger people may well remember Alan Rickman for his role in Harry Potter, older generations will remember him for his ability to play almost any part. Sense and Sensibility, Sweeney Todd, these are just some of the movies he will be remembered for. He was a great villain, but overall he will be remembered for his diversity.