I have a paranoid fear that if something happens to DH, it will take ages before I am contacted.
There is no particular reason that he would be more likely to be in an accident than anyone else.
I wrote emergency contact information for us on index cards, to be folded and put in our wallets. DH thought his card was messy because it didn't fit in his wallet without folding; I'm guessing that he still carries it but I'm not 100% sure.
DH said that if anything happened to him, someone would look at the address book in his mobile phone to find someone to call - but there are a lot of people besides me in his address book.
I think part of my paranoia comes from the fact that before I moved to the UK, people where I lived (New York City) carried around photo ID, such as a driving license all the time.
A lot of it just has to do with paranoia that comes from living in a place that you didn't grow up in and not knowing how things are done.
Also, things just seem to be a lot slower around here. When we were having problems with asbo kids around my old block of flats, we had a community meeting which included the police, and we were told that if you reported someone trespassing, committing vandalism, harassing or threatening, others, etc., the guaranteed response time was within 24 hours! (I assume that if someone's life was in danger, the response would be somewhat quicker.)
The only somewhat similar experience that I had in the US was when I was with my ex, and we were both going to the same university. I was in the library and one of the security guards came to me and found me and told me that my ex had been in a car accident (turned out to be not very serious). I was informed very soon after the accident happened. But my ex was conscious so probably described me and told someone where I would probably be and asked them to find me.