I was a sophomore in college and living in a house with some friends off-campus at the time. I was doing my morning email & website check when one of my friends IM'd me telling me to turn on the television (any channel, didn't matter). I stumbled downstairs, turned on the TV and flopped down on the futon.
As soon as I saw what was happening, I picked up the phone and called my parents to let them know. Shortly after my mom picked up, the first tower fell. I stayed on the phone through the second tower falling. After a while, my phone battery started to die so I hung up and spent the rest of the morning fixed to the TV. As my roommates woke up I updated them on what was happening and by mid-morning everyone in the house was watching. One of my roommates had a brother living in NYC. He spent all day trying to reach him but the phones were jammed. None of us made it as far as showering or having breakfast, we were all still in our PJs.
I completely forgot about class and work that day. But it turns out so did almost everyone else. Going back the next day it turned out none of the professors made it to class, and most of the lab staff never showed up to open the lab that morning so no work got done anyway.
It was an incredibly surreal day for me as I had never really lived through anything like it. The plane hijackings of the 70s were before I was born, and I was too young for the ones in the 80s to have much impact. The first WTC bombing was a vague memory, but since the towers didn't fall, it didn't stick too well. To me, the idea of terrorism was something remote and academic up to that point.
Without a doubt, a defining moment for me.