The Herald of Free Enterprise disaster- I had had some friends round for tea for my 13th birthday, my dad was driving one of them home and I went along for the ride- it came over the car radio.
(This one has become infamous, because it's the How I Met my Oldest Friend anecdote)- there was a knock on the door of the shared house I was living in in London at the age of 17, and I opened the door to another 17 year old standing on the doorstep saying "Did you just hear a bang?!" That was the IRA bombing the Baltic Exchange.
9/11: I was browsing the shelves in a second hand bookshop in Stroud, and the owner was on the phone: "No! Oh my god!!" and then turned the radio on. I initially thought it was a play.....
The death of Diana: I was working in a club in Switzerland and the night previously I'd had a rant about her to one of the locals: "spoilt, parasite" etc etc. The next night he came in and said "I hear your favourite person's dead then!" I thought he was joking initially.
7/7: I had a job taking American high school groups around Europe- heavy on the London and Paris. We used to take the kids around on the tube all the time. I'd left London with a group on 5/7, done the 2 days in Paris and seen them off at the airport and gone back to my hotel. I switched on the French news and at first couldn't make sense of it all- "Why are the Eurostars to London cancelled?". Then gradually pieced it together. I'm still grateful I wasn't looking after a group in London on that day.
MH370- we were just about to fly home from Morocco. I'm a nervous flyer at the best of times.