In 50 years since my first flight, I've had delayed bags 4 or 5 times and I've always chalked it up to "meh, stuff happens". Of course the only time it might have been serious was when I was going for an interview day while I was in grad school, but that time the bag caught up with me at the hotel overnight. The other times I was either young or on my way home (one time DL sent my bag to DFW rather than DTW).

Worst I heard of was one time the CEO of my company was on a RTW business trip and BA lost track of his bag on a nonstop DTW-LHR. The bag caught up with him about a week later in Beijing.