I was four and was living in California. Believe it or not, I actually remember that morning.
The moment the first plane hit, I was asleep (It was about 6am). The house phone rang, waking me up, but I stayed in bed. I heard my mom answer it (It was my Aunt calling, she lived in NYC at the time, but not in Manhattan), and then heard something along the lines of "Oh my god, you need to get out of there..."
My four year old mind had no idea what was going on, so when my mom and dad started talking quietly, I got kind of nervous. My aunt was still on the phone when the 2nd plane hit, and I guess I must've made some noise because my dad came in to check on me. He told me that some bad guys crashed a plane in NYC, and that everyone was okay, and to go back to sleep. As a four year old with no sense of what actually happens when a plane crashes, I believed him and went back to sleep.