First of all? BLADE RUNNER in and of itself is an ICONIC film in its own right and that's not just me saying it. That fact is known the world over.
Rutger Hauer is known best for the TEARS IN RAIN monologue from BLADE RUNNER which he wrote mostly himself. I think the scene is iconic because Roy is originally depicted as the villain of the movie along with all his other now deceased replicant family members. By now, he's dying and in fact, he's about to die any second. He attempts to explain to Deckard the things he's seen. The subtext, which will be different to many and that's the beauty of film and subtext in dialogue; is that he's telling Deckard how PRECIOUS life really is and that maybe... Just maybe? Humans simply take it for granted. He may be a Replicant but as we can plainly see in the film, he loves his family of Replicants... Especially, Priss.
Replicants were built to be nothing more than slaves... Deckard knows this... Which is another reason why he can kill them so easily. No remorse.
Roy doesn't want to die. Why? Because even as a Replicant being chased by a BLADE RUNNER, life is worth living. He's experienced so much in so little time that he wants MORE hence, his visit to Tyrell and even though Roy kills Tyrell, I feel that it's this particular scene that now shows us Tyrell as the villain.
Deckard is just a guy doing his job up until the TEARS IN RAIN scene. To him? Replicants are nothing. Just something he needs to kill. Roy saves Deckard before he falls to his death. In other words, he's proving his HUMANITY to Deckard. That he is in fact REAL and not just some device dreamed up in some laboratory. Deckard INTENTLY listens to Roy before he dies and to me? He finally GETS IT. No matter what these replicants were created for? They TRANSCENDED above and beyond that. They are now as human as human can be.
Which is why Deckard takes off with Rachael in the end. Although, some argue that Deckard too, is a replicant and that could also explain why he takes off with Rachael. The beauty of the film however, is that we simply do not know for sure. Each of us will have our own opinion and I think it's these differing opinions that we can talk about with each other that help give the film and the TEARS IN RAIN scene its iconic reputation.