I remember when Helen Keller and Bobby Kennedy died, both in June, 1968. I was 7. I knew that Helen Keller had something to do with being blind, but I had no idea who Bobby Kennedy was. I just remember my older sister waking me up one morning saying “Senator Kennedy’s been shot!” (although he was probably already dead by morning).
The earliest one I remember is Elvis. It didn’t really affect me. I just remember all the news coverage. We were in England at the time, and they were showing scenes of crying people. I remember wondering if everyone in the US had gone crazy. Mom had to tell me who he was.
John Lennon’s death was the first one that I saw affect people first hand. I was in high school at the time, and many of my classmates were really upset. I wasn’t, but then I was never affected by celebrity deaths…
…until Mr. Rogers. Damn. He should have been immortal.
The first famous death I recall was a multiple: the Challenger disaster when I was 10 (in 1986). We were going to get to watch the shuttle launch on TV in school that day, but I got sick and stayed home, so I was watching a soap opera with my Grandma instead of watching the launch. When they broke in to announce the explosion I thought that if I had watched it like I was supposed to they would have been fine, but my inattention had allowed the shuttle to blow up.
I never had much of a problem with low self-esteem as a child. 
matt_mcl, that is a horrible thing to think! The Great One is eternal!