I know too many people who had this happen...

I have an electronic book (backed up of course).

I have photocopies of my paper logbook.

My original logbooks (with endorsements) live in a fireproof safe, which is bolted to my floor. If you can't afford a safe put them in a double-ziplock bag in your freezer. Thieves probably won't look there, and the insulation will likely protect against a fire.

If my original logbook is out of the safe, it is physically on my person the whole time...not left in cars, luggage, hotel rooms, etc. Unfortunately, our logbooks seem to appear valuable to stupid people.