Are shields useful in Final Fantasy 3?
Solution 1:
The main purpose of a shield is to just improve your defense (and maybe also get extra benefits for specific shields). In the majority of cases, the best defense is a good offense. So wielding two weapons will kill off enemies faster than they can kill you.
Shields then serve to reduce damage when damage is inevitable. And to that end, it's best on defensively minded classes that will be protecting all your allies who do have two weapons. These would be the Knight, and in the DS/iOS remake the Viking. All mention of Viking beyond this point refers to the remakes, as the original Vikings did not get a special skill.
The Knight's Cover
ability lets it take damage in place of weak allies. Meanwhile, in the remakes, the Viking gains the Provoke
ability which expends its turn to attract attacks. Since this means they'll be the ones taking damage, equipping them with shields is usually a good idea so that they can take more damage.
Vikings in particular, an actual common strategy is dual wielding shields. Since Provoke takes up your turn, you won't be attacking. Two shields gives you a whole lot more defense, your axes and hammers tend to miss anyway and you don't have nearly as strong an offense as the more attack-geared classes. So, you could have a powerful party of attackers that can safely attack while one dual-shielded Viking takes all the hits. This is especially helpful for those bosses who throw in an extra physical attack on their turns.