I was flying DTW-CDG and sat next to an anxious woman who seemed fine until we passed Newfoundland and completely came unglued. Rocked back and forth in her seat, crying, saying "I don't want to drown if we crash, I don't want to drown if we crash." I'm an ER/Trauma nurse and I deal with people who have anxiety attacks all the time and it really sort of annoyed me that I had to deal with one on a transatlantic flight. I asked her if she had any anti-anxiety meds on her. She did but of course they were in her checked bags. Who does that? I just looked at her and said,"Well the good thing is if we crash you'll be dead when we hit the water so you won't need to worry about drowning. Why don't you pull down the shade, listen to some nice calming music and pull yourself together or this is going to be an awfully long flight for both of us." I offered her my Bose noise cancelling headphones so she wouldn't be overdramatic at the various sounds of flight. She followed my advice and in 20 minutes she was snoozing.
Those prone to anxiety really need to pre-plan to have their meds on them (and not in their checked bags) and if they're terrified to fly, then DON'T. Its awfully rude to inconvenience others because of your illness. If I had a stomach virus and was vomiting, I wouldn't think twice about not flying.