I'll get this started. For myself, born the year that the concentration camps were closed (1945), I remember learning about it first as a child. We didn't know all that much. A lot of Holocaust experiences were repressed at that time - survivors had no one who wanted to listen. But we were aware that my maternal grandmother, who arrived in the U.S. around 1913, lost her parents, brothers, sisters--all her relatives - we felt her sadness. Then something happened in my teenage years that catalyzed my interest. In the early 1960s, we heard that my grandmother's youngest brother had actually survived the Holocaust (where he lost his first family) and had emigrated to Canada. Despite strict immigration quotas, Nachman and his new family finally arrived in the U.S. after living in Brazil for 10 years. I had both living survivors and living reminders of the Holocaust in my own extended family.
I think that my awareness of the Holocaust did increase my feelings that we needed an "Israel" as a safe haven. During a recent visit to Israel, I was struck by how much the Holocaust is emphasized there now. I remember a time when even in Israel (especially in Israel) it was a forbidden topic. I think now it is being used in order to revitalize flagging national purpose and fatigue experienced particularly by the young people there. But I think that what I was struck by was presence of fear - perhaps a fear brought over by the Holocaust generation, transmitted down through subsequent generations, and exacerbated by Israel's isolation. So whenever I judge Israeli government actions, I keep in mind this fear. I think it's a large factor in Israeli life and politics.