Happened to me only once
I was flying from Detroit to Dallas, and someone on the plane fell down and cut their head. First they asked if a doctor could volunteer his/her assistance, then they said we were being 'expedited' into DFW. Two things I remember about this: heading straight into DFW cut 30 minutes off of a two hour flight, and I was AMAZED at how fast an MD-80 could corner on the ground. Passenger looked dinged but okay (and embarrased) when they wheeled him off.