What is the units digit of 1! + 2! + 3! + … + 100! ?

From 5! onwards every factorial contains $2\times 5=10$, so each ends in 0 and adds nothing to the units digit. Only 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33 matters, so the units digit is 3.