Without your memories, you would probably just be swimming in a puddle of your own drool. They're kind of the key to everything: if you literally didn't have a past, you would have no idea how to behave in the present.
This is the problem the replicants face in Blade Runner. Initially, they don't have memories of the past, which makes them emotionally inexperienced—they react weirdly to things—they might sympathize more with an oyster than with a dog, for instance. But the Tyrell Corporation creates Rachael as an experiment, to see if they can make a more balanced replicant. She has fake memories implanted, which cushion her responses to things and make her act relatively normally. So do her "fake" memories make her more "human"?
Questions About Memory
If you woke up without any memories, how do you think you would act? Could you end up turning into an entirely different person?
How have your own memories formed your sense of identity? When you think of who you are, what memories do you think of first?
Why does Deckard have so many family photos sitting on his piano? Are they all part of his constructed identity as a replicant? Or are they real?
Has Roy managed to create his own unique identity, using memories collected during a mere four-year lifespan? How does his dying speech seem to imply this?
Chew on This
"Without memory, there is no culture. Without memory there would be no civilization, no society, no future." – Elie Wiesel
"Happiness is good health and a bad memory." – Albert Schweitzer