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In Diablo 3 each class has a primary stat that increases all their damage. They also seem to have very minor side benefits such as a bit of dodge for dex, however the amount of dex a barb would need to make this valuable seems to be a pull from focusing on Strength (or vitality).
Is there any situations where it would warrant wanting stats that are not your primary?
Strength increases your Armor by 1 point per point.
Dexterity increases your dodge chance by 0.01%-0.1% per point.
Intelligence increases all resistances by .1 per point.
This has a number of interesting effects - most notably, because of the way Resistance works (it's functionally identical to Armor), stacking small amounts of Int on a Barbarian, Demon Hunter, or Monk can result in a dramatic survivability increase.
Resistance, like Armor, will reduce all damage you take, and, like armor, you gain substantially larger marginal benefit by increasing it when you don't have much. Since typically, a Monk (for example), will have a reasonably high Armor stat from gear and passives, and very low Int, adding just a little bit of Int via an oddly itemized piece of gear can provide a really large survivability boost - certainly more of one than trying to add Armor via Strength.
However, because everyone has a decent amount of Armor inherent in their items, increasing Strength for a similar benefit is generally not worthwhile unless you're playing a Barbarian that wants the damage boost as well, or a Wizard or Witch Doctor with a very high Resistance stat already.
