I was just three years of age at the time, but I carry vivid memories of watching the first 'Daleks' story on the CBC in... 1965.
We Canadians were lucky: In this country, the CBC (Canadian Broadcasting Corporation) premiered Doctor Who's first story in January of 1965. According to my research, the network never repeated the series' first-season episodes, and this bit of trivia allowed me to peg my earliest DW memories to February of 1965: "The Daleks", Who's second story, scared me somewhat silly but my mother was there to change the channel on the Admiral television set whenever I yelled: "Mum!" ("I wish you'd make up your mind, dear. I can't keep changing the channel for you.")
I will soon upload a "Doctor Who and Me" piece.