Elemental damage is extremely common in RPG's, particularly turn based and Japanese RPG's. Rather than have damage be damage, many attacks do damage of a specific type, and many enemies (and often the player characters as well) take more or less damage from certain types of damage. Potentially, a well implemented system of elemental damage can add a dynamic strategic element to an RPG, but these systems are pretty much always poorly implemented.
Consider Final Fantasy X. The black mage of your party, Lulu, for the majority of the game, has only as many as 12 useful spells: a damage dealing spell in each of the four elements (fire, thunder, water, blizzard), each with three tiers of strength. Her other spells and basic attack are useless, and using items is rarely the right choice in combat, so whenever Lulu's turn comes up, the only questions you need to ask yourself are "How many magic points can I afford to spend?", "Which enemy is my highest priority to kill?", and "What spell will do the most damage?". The first two questions are sometimes a little tricky, but the last one never is. Spells of different elements within the same tier of power differ only in what type of damage they do. They cost the same amount of magic points and do the same base damage, so the best spell to use is always the one that does the most damage, which is rarely difficult to figure out. For example, if you're climbing an icy peak in the middle of the frigid Northlands, chances are pretty good that everything is weak against fire. Some bosses try to be tricky and change what element they're weak to, but they're never very sneaky about it. You generally don't even need to spend a turn to find out what the boss's new weakness is. All this does is make sure that the player isn't falling asleep. Towards the end of the game, you get access to spells that deal non-elemental damage, so they deal full damage regardless of the enemy's type. This should make things much simpler, but it really doesn't detract from the strategic elements of the game since choosing which spell to use is basically a non-choice to begin with. Part of the problem is that the spells differ only in the type of damage you do, and you almost always have equal access to spells of all four elements. If you didn't have equal access to different types of attacks, and there was a less arbitrary reason why different attacks did more or less damage to different enemies, you might have to make some more interesting choices.
Consider Paper Mario: The Thousand Year Door. Damage is damage. You don't have to check if your enemies are weak against fire or ice damage, crushing or piercing damage. Damage is damage. But that doesn't mean that all attacks are equally effective against all enemies. Whenever you attack an enemy, the damage you deal is reduced by their defense. Let's say you deal 8 damage, they have 2 defense, 8-2=6, so you deal 6 damage. However, if you have an attack that hits multiple times, your opponent's defense is applied for each hit. For example, if you have an attack that hits 2 times for 4 damage each, and your enemy still has 2 defense, you deal (4-2)+(4-2)=4 damage. So multi-hit attacks don't do so well against enemies with high defense. However, if you have a bonus to your attack, from an item or from your equipment, it's applied to all of your attacks. So, let's say you get +3 to your attacks, and your enemies still have 2 defense, your 2-hit attacks (assuming you still have 4 base damage) will deal (4+3-2)+(4+3-2)=10 damage. In paper Mario 2, you almost always have the choice between using 1-hit attacks or 2-hit attacks (or sometimes attacks with more hits), but depending on what gear you equip Mario with, you will be more capable of doing one over the other. The moral of the story here is that if you have more bonus damage than your opponent has defense, you are better off with multi-hit attacks. Otherwise, you should stick with 1-hit attacks. Therefore, in every area you adventure through, an important question you must ask yourself is "Am I capable of boosting my attack bonus higher than my enemies' defense, and what will I have to compromise to get my attack bonus that high?"
I'm not trying to say that any battle system using elemental damage is bad, just that there are a lot of wrong ways to do it. For an example of a game that handles elemental damage pretty well, consider Final Fantasy: Chaos Rings. In that game, there are only 3 elements, which, for clarity, I'm going to call rock, paper, and scissors. Square has a problem with giving unfamiliar names to intuitive concepts. Enemies come in all three flavors, and are weak or strong to other elements exactly how you'd expect them to be. A rock elemental attack will deal more damage to a scissors elemental monster, and less damage to a paper elemental monster. You do have the option to equip yourself with spells of each type at the same time, but the total number of skills and abilities you can have equipped at once is strictly limited, so in order to get that extra bit of versatility, you might need to compromise your character in other ways. What makes things really interesting though, is that after you cast an elemental spell in battle, your character gains an affinity for that element until the end of the battle, or until you cast another elemental spell. So if you cast a rock spell, that character's physical attacks will deal extra damage to scissors monsters, and reduced damage to paper monsters. That character will also take extra damage from paper monsters, and reduced damage from scissors monsters. If all of the monsters you're fighting against are of the same type, it's pretty easy to brace yourself with the right element, but battles are rarely so simple. It is more often the case that you will be fighting a rock monster and two scissors monsters. You could use paper magic to kill the rock monster quickly, but then the two scissors monsters will tear through your party. It would probably be better to use rock magic to kill the scissors monsters, leaving you on even footing with the rock monster. However, if the rock monster was 4 times more dangerous than the scissors monsters, then you might still be better off using paper magic to kill the rock monster before dealing with the scissors monsters.
Things get even more complicated during boss fights, since bosses generally have access to all 3 elements, which makes them very good at exploiting the player's weaknesses. Unfortunately, by midway through the game I had learned a few abilities which, when used together, enabled me to deal enormous amounts of non-elemental damage without gaining any elemental affinity, entirely sidestepping the game's elemental damage. Not only was this a much simpler way of beating bosses, but it was also much, much faster. I suppose I have only myself to blame for choosing to exploit such tactics, but I still think that Square should think a little harder about how they want people to play their games. But still. Points for trying.
