It's obvious that toghness reduces damage from a rolled attack. But there are a couple of other sources of damage where it's less obvious what happens.

1) Dogs of war. If the first roll is a "valor" then the target takes "one hit which can not be ignored ". Does "not be ignored" mean that a unit with toughness still takes damage from this effect. ?

2) One of the commander's has a tactic which causes "1 damage to each engaged enemy unit" Does toughness-1 block that damage ?

1. Yes, the unit with Toughness still takes the hit. The "cannot be ignored" is the indicator that it trumps those things which ignore hits, like Toughness.

2. Toughness "allow units to ignore X hits before any figures are removed from the target unit", so if the ability causes hits and does not state that the hit cannot be ignored, then yes, it blocks the damage.