When I made reservations this year in Bizelite to NRT, the reservationist tried to convince me that an e-ticket is much better than a paper ticket. The big benefit is that unlike a paper ticket, you can't lose an e-ticket. I listened to her pitch, then told her about the horror story I witnessed at FCO last year, while checking in for a flight to JFK. The gentleman in front of me at the Bizelite counter handed his passport to the counter agent, told him he had a reservation on the flight to JFK and was informed that no reservation was on record! She asked him for his record number...like most of us memorize it, then said she would issue him a new paper ticket at the full fare price. Needless to say he went ballistic! He asked for the supervisor but was told she is on break. I don't know what happened next as it was my turn. I breathed a sigh of relief when I went to the counter with my "paper" ticket and was processed with no problem.
She told me that was an isolated incident, the computers were probably down, etc., etc. I smiled and said thanks, but no thanks, and she issued me a paper ticket. On domestic segs, I use e-tickets but not on international segments. And, when using e-tickets I always keep my record number, just in case.