I always have the numbers with me, but barring some problem with the typing in of my name, I don't know why I bother. If the system doesn't have my reservation, having the reservation number isn't going to magically restore the reservation to the system. I've found that if a situation like that occurs, and they can fit us in, they'll do their darndest to do so. And if they cannot fit us in, having the number will likely not make much of a difference.