In the last 3 NASA classes, we've actually had a fairly even split of civilian to military. However, the key is that is just general military - the days of it being exclusively reserved for pilots are long gone. In the last few classes, we've had a Nuke and a SEAL for example. And in only a few classes earlier, we've had a diver as well. I believe an oceanographer too.
Big thing people need to remember is that it costs a lot of money per pound to send up into LEO, and so if you want to send a human up, you need to be a damn good bang for the buck deal -- which often means that you've got a big brain in some field that NASA wants to have for experiments or whatever else is on their plate (and hence why if you don't have at the very least a degree from engineering/science/some other heavy technical field.... good luck)