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.
Best Answer
More information about the job guide that you can read. The following information below here will answer your general questions about job levels.
Q: What is Job Level?
A: Job Level (Job LV) is a renewed idea for the DS version. Each character can have, at most, 23 jobs, and every Job comes with a Job LV showing how proficient that specific character is at that Job. Maximum Job LV is 99.
Q: What does Job LV do?
A: The more you train as that Job, the higher the level will become, and the better your character will perform! Here is EVERYTHING that Job LV affects:
Q: What is NOT affected by Job LV?
A: The characters' overall stats are not affected by Job LV. Strength, Agility, Vitality, Intellect, and Mind.
Two characters with SAME Job and Character LV, but different Job level, will have the same stats. However, their performance may differ.
Q: Speaking of the Job Mastery Items, can I get more than one?
A: There is ONE item per Job, and you can only get each of them once. In the end you can only have 23 of them.
Q: How does the Job LV increase?
A: Every character has a hidden stat called Job Points (JP) that dictates their Job LV growth. When JP is accumulated to 99, Job level goes up by 1. Each action (except: Front, Back, Escape, and Flee) will contribute a fixed amount of job points to the character.