There is no reason to ever use a standard attack as a Barbarian, or any other character. The design philosophy that the team was aiming for was to allow people to use skills as much as possible, as that is the most satisfying way of taking out the baddies. Obviously this is somewhat limited by the resource systems set in place, but since the Barbarian, Monk and Demon Hunter all have resource generating skills, and the Witch Doctor and Wizard both have low to zero cost skills, it's obvious that Blizzard wanted people to use skills as their primary attacks, and not just swinging a weapon.
However, there is nothing stopping you from using a standard attack. Given that we've not seen content past Act 1 normal, there may be situations where killing multiple enemies at once is a bad choice, and if your default attack is bound to an AOE ability, (e.g. Cleave for the Barbarian, Crippling Wave for the Monk, etc.) you may be left to using a default attack.