I don't think those kinds of shows are unique to the US - 24 Hours in A&E is very popular here in the UK:

http://en.wikipedia.org/wiki/24_Hours_in_A%26E

Of course, with the NHS there is a general feel good factor in that we get to see our tax money being used to do good. Indeed I have seen criticisms of 24 Hours in A&E that because it generally shows the NHS is a positive light and as the NHS is pretty unashamedly a socialist endeavor that shows likes this are politically biased!