In FF4 characters were left and right handed, so if you equipped their weapons to the wrong hands, the attack power would be reduced. I remember Rosa and bows always meesed me up. Which hand uses the bow, and which one uses the arrows? I think Yang (Monk class) and Edge (Ninja class) were both ambidextrous, so it didn't matter what hand you used, and they were also capable of dual wielding. Although I don't think Yang was even capable of equipping a shield, and his claw weapons basically just added elemental power to his attacks.
In FF5, all Ninjas naturally had the ability to dual wield, and after you learned a special Ninja ability you could use that talent in any form (also it was automatically added to your basic form). I don't think Monks could equip anything on their hands without a special ability.
In FF6, Shadow (the Ninja) was probably able to dual weild. And I think Sabin (a Monk) was only able to equip claws on one hand. But anyone in the game was able to dual wield, provided they had the "Genji Glove" relic equipped.