I think the first notable celebrity death for me was Elvis. I was 10 at the time (turning 11 the next month) and actually knew who he was.
I was about four months pregnant with my first son when Princess Diana died. I watched her funeral on TV. The boys walking with her coffin was a heartbreaking image.
My day usually starts around PST 05:00, I remember watching the news and then breaking story of the 9/11 attacks. I immediately called my kid's aunt in New York but the line was busy and constantly busy throughout the day. She eventually sent an email to the family around 20:00 letting us know their family were all okay. The kid's uncle followed up with an email around midnight about his experience that day. He was working a few blocks away and had a clear view of the World Trade Centre.
Like Sir Creep, I remember the 1986 Space Shuttle explosion as well. I was home sick. I didn't see it live, but got a call from my BF at the time to turn on the news. All those children tuned in to watch the teacher in space, what a terrible thing to witness.
I'll finish with Robin Williams, while driving home from work I heard the announcement on the radio and I had to pull over because I started to cry. It is usuallywith morbid facination that I follow celebrity deaths, but his death hit me hard.