Legend of Fae
divides its gameplay into two parts, the puzzle-based mana-gathering half of the screen, and the story portion. The game takes place in a world where magical creatures, the Fae, are breaking into our realm and the only way to stop them seems to be a lantern left by a girl's mentor and guardian just before disappearing.
On the lantern is the game board where she can manipulate orbs to gather different kinds of magical elements. These are used so that she can power her four new mystical friends and allow them to attack the various enemy creatures that attack her. As you might expect, these elements are Earth, Wind, Water and Fire (all we need is some Heart before we can summon Captain Planet). By swapping orbs on the board and lining up three or more, she adds to the amount of mana she has and with various mouse clicks on the story-half of the screen can send the different elementals against different enemies.
Predictably enough, the enemies also have an elemental slant and the key to doing the most damage comes in knowing which elements have power over which other ones. Water trumps Fire, which trumps Earth, which trumps Wind which takes out Water (though I'm not exactly sure why for that last one).
There are other orbs as well. While not in a battle, you play the game in order to regain magic as well as physically walk down the side-scroller area your character is traversing. The same tiles that move you can also be used in battles in order to dodge attacks.
There is also an upgrade system in place to allow your elemental attacks to do more damage or increase your defense, attack, speed and mana-gathering, but there doesn't seem to be any real reason to specialize in any particular element. In fact, since you are regularly attacked by mixed types of enemies, it is recommended that you try and level everything up as evenly as possible.