At various points in the campaign, you will come across safes. Some missions have more than one safe, and safes may open to more than one combination. Below, you will find known combinations for the corresponding safe:

Mission 1 - 451
Mission 2 - 287 (Dr. Galvani's house)
Mission 2 - 217 (kennel door)
Mission 2 - 203 (Overseer's base)
Mission 3 - 138, 656, 679, 696, 879 (Slackjaw quest)
Mission 3 - 656, 696 (artist's house)
Mission 4 - 437 or 473 (building top floor)
Mission 4 - 294 (behind painting)
Mission 6 - 935 (Lord Regent's quarters)
Mission 7 - 428, 525, 528, 628