Keep it up to date and legible! You never know when you might need to produce it - maybe for future employment. The S.E.Asian carrier that 411A refers to (I think) is well known for adding up each applicants log-book entries and delighting in pointing out an addition mistake some thousand of hours previously! Mine was 2 hours out 12 years ago! A correct log-book was a pre-requisite to advancement to the next stage of the interview process.
I have also had to refer back to my log-book with regard to an incident (I was able to say "t'was not me, I was elsewhere and not on that particular aircraft".