I use logbook pro. My paper log isn't even close to current, but I log my flights in logbook pro every leg. I keep multiple backups, including a backup copy uploaded to an off site FTP sever. I've got backups on 2 separate computers too. So if anything crashes, I won't be out too much information.

A paper log can always burn up in a fire. Electronic is easily transferred offsite, saved, stored, and accessed. Considering the year we are in, I think electronic is perfectly safe as a sole means.