I've been involved in four such actions, all on a small but deadly scale and have witnessed two involving a fairly large number of combatants on both sides with bayonets and rifle butts as well as hands and feet. I know of half a dozen others involving various numbers from reliable sources.

As mentioned, aside from those incidents, I've been involved in or witnessed dozens of detainee or PW dustups where physical means had to be used to effect the capture or transport. As Wilf says, that is not hand to hand combat but it does require some training. Have a Son who is an in-service training Officer in a mid size police department and his defensive tactics classes are oriented to not using excessive force...

The hand to hand action in military combat is very much type of unit and operation dependent, no question -- but given bad circumstances it can involve anyone who serves and it is a facet of training wherein the psychological benefit to those trained is very beneficial and the skills gained are generally dire emergency items one hopes will not be used. Most will not use those skills; the few who have to will be glad they have them...

An interesting aside on this is that the current batch of 18-20 year olds in the US generally has little experience of physical contact (to include sports) and tend to be contact averse, this has caused not only the Armed forces but the Police to have to strengthen their combatives training just to counter this trend.