Not even Puzzle Quest goes without them. Normal bats can be quite annoying, but the real Goddamned Bats depend on your class choice. For instance, Fire Elementals are Goddamned Bats for a Wizard due to their high fire resistance, and the fact that they can drain your entire red mana pool and heal themselves for every point. In fact, anything with some resistance borders on this since the resistance works against any spells that use the respective kind of mana, and most likely half of your spells. And for extra fun, resisted spells end your turn even if that spell normally wouldn't.
And for the added "That Makes No Sense" award, enemies would often resist spells that you were clearly casting on yourself!
Puzzle Quest 2 follows up with the Ghost and Vampiric Mist enemies. Both share a permanent status ("Intangible") that randomly nerfs damage done down to 25%. The Ghost spams a spell that fills the board with blue gems, which can lead to them getting several turns in a row. The Mist has low hit points (maxes out at about 65) and low offensive strength, but also has a spell that can heal itself while draining your purple mana gauge and a second spell that temporarily locks out your spells and weapons. While neither enemy is particularly hard, they can take forever to defeat.