My first flight alone was JFK-LAX on a TWA 747, when I was 14 (April 1996). Turned out that my school's spring vacation coincided with a business trip of my father's, but he had to leave a few days before me. I was excited both because I was flying as an "adult" for the first time but because I was also going to JFK on my own! I took the school bus home and then took some sort of shared-ride service (Connecticut Limo, I think) from our house in the suburbs right to the airport. I remember the old TWA terminal quite well, and the fact that I had a paper ticket with the "boarding pass" stub on the end. There were dozens of those supposedly deaf solicitors selling trinkets inside the gate area, which annoyed me greatly. My dad deliberately booked me on a 747 as he's always been somewhat fearful of flying and thought that the 747 was the safest plane because of its size.
We flew a very northern route...I saw several of the Great Lakes and could pick up Minnesota FM stations from my Walkman inflight. The flight attendants took good care of me and brought me two meals at dinnertime (I had the same appetite at 14 as I do at 25, but now all there'd be on a JFK-LAX in coach is buy-on-board!

) The flight was not that turbulent, but upon landing at LAX I threw up all over my brand new green shirt. After everyone else had deplaned, an FA got my bag and found another shirt for me, but I'll never forget my embarassment at that moment. Dad met me at the gate and we went to the hotel in a rented Olds Achieva.
I flew LGA-ATL a few times in high school alone to visit my grandmother, and of course many flights alone in college.