Personally, I've got two logbooks that the military has filled out for me during my flying time with them. But I also keep an electronic log book because on occasion I do some civilian flying. For some reason the military doesn't actually put that in my logs. I just make sure that I fill in the correct information for each flight (yes, I'm a nerd, I've got it broken down that far!). Plus, I figure if I ever go and get my CFI or any other instructor rating, I can print the thing out and have my instructors endorse it for the myriad things that need endorsement.
I have yet to interview for a civilian flying job as my time in the military is coming to an end, but most of the gentlemen I know who are reservists and fly for airlines said they think I've got a good idea keeping my own log.