FFIV
Bloodfeast - Minor non-elemental damage to one enemy in addition to the Sap status.
Bad Breath - Inflicts multiple status ailments to one enemy.
Constrict - Inflicts Paralyze on one enemy.
Slap - Inflicts either Paralyze or Curse on one enemy.
Blaster - Inflicts either Paralyze or Death on one enemy.
Stone Gaze - Inflicts Gradual Petrify on one enemy.
Stone Touch - Inflicts Gradual Petrify on one enemy.
Hex - Inflicts Pig status on one enemy.
Glare - Inflicts Confuse on one enemy.
Wing Scales - Inflicts Blind on one enemy.
Tongue - Inflicts Sleep on one enemy.
Bile - Poison damage on one enemy.
Gaze - Inflicts either Confuse, Sleep, or Paralyze on one enemy.
Sleeping Gas - Randomly inflicts Sleep on one or all enemies.
Poison Gas - Randomly inflicts minor non-elemental damage and Poison on one or all enemies.
Curse - Randomly inflicts Curse on one or all enemies.
Pollen - Minor non-elemental damage to all enemies in addition to the Sap status.
Flamethrower - Minor Fire-elemental damage to all enemies.
Blaze - Fire-elemental damage to all enemies.
Frost Blast - Ice-elemental damage to all enemies.
Lightning - Thunder-elemental damage to all enemies.
Earthquake - Non-elemental damage to all enemies.
Thermal Rays - Non-elemental damage to all enemies.
23 skills. Only 2 of them are about dealing straight non-elemental damage. The rest are skills with status effects and elemental properties.
FFV
Doom - Kills one enemy after 30 seconds.
Roulette - Kills one random ally or enemy.
Aqua Breath - Deals non-elemental damage to all enemies. Deals 8 times the damage to desert enemies.
Level 5 Death - Kills enemies whose levels are a multiple of 5. Ignores death resistance.
Level 4 Graviga - Casts Graviga on enemies whose levels are a multiple of 4.
Level 2 Old - Inflicts Old on enemies whose levels are a multiple of 2.
Level 3 Flare - Casts Flare on enemies whose levels are a multiple of 3.
Pond's Chorus - Inflicts Toad on one target.
Lilliputian Lyric - Inflicts Mini on one target.
Flash - Inflicts Blind on all enemies.
Time Slip - Inflicts Old and Sleep on one target.
Moon Flute - Inflicts Berserk on all allies.
Death Claw - Reduces a target's HP to single digits and inflicts Paralyze.
Aero - Deals Wind-elemental damage to one or all enemies.
Aera - Deals Wind-elemental damage to one or all enemies.
Aeroga - Deals Wind-elemental damage to one or all enemies.
Flame Thrower - Deals Fire-elemental damage to one enemy.
Goblin Punch - Deals non-elemental damage to one target. If the target's level is same as the caster's level, deals 8 times the damage instead. Ignores row positions and weapons' special effects.
Dark Spark - Halves the target's current level.
Off-Guard - Halves the target's Defense.
Transfusion - Sacrifices the caster and fully restores one target's HP and MP.
Mind Blast - Deals non-elemental damage while inflicts Sap and Paralyze to one target.
Vampire - Absorbs HP from target and restores caster's HP.
Magic Hammer - Halves target's MP.
Mighty Guard - Grants Protect, Shell, Float to the party.
Self-Destruct - Kills caster to deal non-elemental piercing damage to one target equal to user's current HP.
???? - Deals non-elemental piercing damage to one target equal to caster's Maximum HP minus their current HP.
1000 Needles - Deals 1000 damage to one target. Damage cannot be reduced.
White Wind - Restores HP to party equal to caster's current HP.
Missile - Reduce target to 1/4 of its current HP.
31 skills. None of them deal non-elemental damage without some sort of gimmick attached to it (ie Aqua Breath, Goblin Punch and 1000 Needles for example). The rest is ALL about status effect, support, level based, or gimmicky.
FFVI
Doom - Inflicts Doom status on target.
Roulette - Randomly select a single enemy or party member, including caster, and inflict Death on them.
Tsunami - Deals Water-elemental damage to all enemies.
Aqua Breath - Deals Water and Wind-elemental damage on all enemies.
Aero - Deals Wind-elemental damage on all enemies.
1000 Needles - Deals exactly 1000 damage on single target. Ignores defense.
Mighty Guard - Casts Protect and Shell to the party.
Revenge Blast - Deals damage on a single enemy equal to caster's maximum HP minus their current HP.
White Wind - Heals all party members including caster an amount of HP equal to caster's HP.
Lv.5 Death - Inflict Death on all enemies with a level that is a multiple of 5.
Lv.4 Flare - Inflict non-elemental damage on all enemies with a level that is a multiple of 4.
Lv.3 Confuse - Inflict Confuse on all enemies with a level that is a multiple of 3.
Reflect??? - Inflicts Blind, Slow, and Silence on all enemies with Reflect status.
Lv.? Holy - Deals Holy-elemental damage on all enemies with a level that is a multiple of last digit of the party's current gil.
Traveler - Deals damage on target equal to number of steps taken throughout the game divided by thirty-two.
Force Field - Chooses a random element and nullifies all attacks of that element, regardless of user.
Dischord - Halves target's level, reducing its stats. Fails on targets immune to Death.
Bad Breath - Inflicts Blind, Poison, Imp, Confuse, Sleep, and Silence on one target.
Transfusion - Caster is removed from battle, restores a single ally to full HP and MP and cures all status ailments.
Rippler - Target and caster exchange all positive and negative statuses. Fails on targets immune to Imp.
Stone - Deals non-elemental damage and Confuse on one or more targets. Deals eight times as much damage on targets the same level as the caster.
Quasar - Deals non-elemental damage on all enemies. Ignores defense.
Grand Delta - Deals non-elemental damage on all enemies. Ignores defense.
Self-Destruct - Caster kills self and inflicts non-elemental damage equal to their HP on a single enemy.
24 skills. Only 2 of them are about dealing straight non-elemental damage. The rest is similar to FFV with status effect, support, level based, etc.