Passports, birth certificates, deeds, and medical records are some of the hardest things to replace quickly if they are lost, so they get a different rule than everything else in the house: they travel with you, and they exist somewhere else too.
Pro tip: A cheap portable fireproof document box doubles as protection during the move and as permanent storage afterward.
Watch out: Important documents packed on the moving truck are at risk of water damage, loss, or theft along with everything else on board.