It's definitely not a requirement to have an electronic logbook.
I know many people just create their own excel spreadsheet and that works great. Like was already mentioned, there is a free one on APC which is pretty good. Another one is LogbookPro...it's expensive, but I bought it a long time ago before I started military flying. It's a great program that has tons of feature that are "nice to have." But the one on APC would probably serve your purpose well.
The reason e-books are nice to have are for the airline applications. The way they want you to break down your time is ridiculous. If you've only flow a few planes in the military, then it's not a big issue, especially if you've only flow single-seat fighters. But if you have multiple aircraft, been a CFI, or SIC...it's gets to be a real headache.
Goodluck.