My experience was not as dramatic as @jon-nyc 's or @bernard 's (and I believe I wrote about this at the old WTF) but I was living in Japan at the time, so it was just before 10pm. I was brushing my teeth and my husband called me into the living room where the news was on TV. (We didn't have a computer at home at that point). I couldn't process what was happening at first, it seemed like a movie, and we watched the rest of it unfold in real time just like the rest of the world. Then I couldn't get a call through to the US for what seemed like forever, I didn't know where my parents were, whether any of my family happened to be traveling (in NYC or elsewhere)... I have family in many places in Western PA, and the Japanese news didn't use any specific place names in their reporting about that part of it. That made me almost lose my mind.
I think being overseas for 9/11 was maybe somewhat similar to being abroad when a family member dies. I felt isolated from the US, and I remember feeling alienated from the Japanese people that were around me (esp at work) in ways I never had before.
In the months that followed I went crazy trying to get American flags to decorate our house. (Which, in a small town in Japan, and before the days of ordering everything online, was not very easy to do). It was another year or more before I made it back to the US for a visit, and when I finally returned, I found a country I did not recognize.