My absolute favourite type is the Megaman Battle Network one.
The jist of the system is have a grid of nine blue tiles and nine red tiles to which everyone is aligned to. You can freely move between your blue tiles, and the enemies can freely move on their red ones. You can either use your inherent attacking ability (in the case of Mega Man this is his normal buster gun), or use "chips". Chips are basically special attacks, which you draw, similarly to a card game. Also like a card game, you compose these decks of chips, and spent the majority of the game collecting new ones, optimising them for the situation. These chips can contain offensive, or defensive in nature, or have support abilities. Remember those blue and red tiles from earlier? You have chips that let you steal a column of tiles of the enemy, giving you more room to move in, and restricting the dodging abilities of the others. Since the tiles on the grid are physical spaces that you use, the game also gives the option to mess with the terrain itself. You can crack or break floors, you can apply elemental properties to them, have conveyor-belts, and all sorts of shenanigans.
Every encounter is rated too, and your battle rewards scale up or down based on your time and combos. Capcom milked this series as hard as they could during the GBA-era, but they had a great idea on their hands, and explored it really well.
