Also, sometimes I like doing as much damage as possible in an RPG.
For example:
Final Fantasy Origins (FF1): I was able to get a monk to do exactly 50976 damage to a frost wolf. (I believe that amount of damage, which is reliable with the right setup, is in fact the maximum possible.) This involves a monk who, without the aid of magic, can do 8000+ damage to most enemies, 6000+ to the final boss (who "only" has 4000 HP), and 3980 to Flans with their insane defense. This is true unless the enemy is hit with a status ailment, in which case some of the monk's attacks miss, leading to lower damage amounts.
Etrian Odyssey 2: I got a Medic to do over 58k damage to a Hedgehog. Further bonuses will cause damage to overflow.
Final Fantasy 5: I was able to get damage overflow to occur here as well. (2-handed + Spellblade (hitting weakness) + level/stat bonuses from bard/mix can cause this to happen.)
Other absurd things I've done:
SaGa 1: I have made most of the bosses die by getting them to run completely out of attacks. (Yes, the game actually keeps track of how many attacks the enemies have left; if the enemy can't attack, it will run away, and if it isn't possible to run from the battle, the enemy will just die.)
Final Fantasy 5: Cast Phoenix without enough MP. When this happens, "Not Enough MP" but the spell's target gets revived anyway. In the GBA version, I was able to get a character to dualcast Phoenix, with the first one appearing to fail completely due to lack of MP, and the second one succeeding. (Undead (from Necromancer) + Dragon's Kiss makes the Phoenix summon have no animation but restore all MP anyway.)