dtgreene: This works when having multiple damage types is favorable, but not when it isn't.
In Final Fantasy 5 and 6, for example, if the target absorbs even just one element of a multi-target attack, the target absorbs them all. For example, if you summon Tritoch (tri-elemental damage to all enemies), and there's an enemy that absorbs ice but is weak against fire, the enemy will absorb the entire attack.
(In FF5, I can only think of one multi-element attack, and it's a Mix that isn't usually worth using, particularly since it requires 2 of the most valuable (non-Elixir) ingredient.)
Enebias: In many new games either in the opposite way than FF5 (example; Spellforce 3, if you have different types of damage only the most effective will be counted) or based on the move you're making (example: Kingdom Comes, where you can stab, slash or pommel strike with the longsword). Some other RPGs like ATOM let you shoose how to use your wepon: if an AK-47 has burst or full auto mode, a knife has stab or slash selection.
Wasteland also lets you choose if you want to fire Single, Burst, or Auto when using a weapon.
Interestingly, if your weapon has no ammo, in Wasteland it behaves like a melee weapon until reloaded (with the exception being that the gun's weapon skill is used for weapon damage rather than Brawling, which still determines the number of attacks).
Does ATOM allow you to use a gun without ammo as a melee weapon? (That is, hitting the enemy with the gun itself, rather than shooting a projectile from the gun.)
By the way, it's also interesting when certain types of attacks behave differently from a mechanical perspective. Final Fantasy 5's Blue Magic has some rather unusual mechanics: Goblin Punch is a physical attack that doex 8x normal damage if the caster's and target's levels are the same, and Level 5 Death is instant death, but only works if the target's level is a multiple of 5. SaGa 1 and 2 have a Chainsaw, which is an instant death attack; whether it can work is determined by the attacker's strength and the defender's defense (and, in SaGa 1, the comparison is not what you'd expect, making it easier to saw apart a god than a goblin).
One could also get some interesting strategy by using an "attack - defense" damage formula for physical attacks, and providing the player with both weak multi-hits and strong single hits. Then multi-hits work well against low defense, but against single targets you want a stronger single hit attack. (The Ranger class in Stranger of Sword City is like that, with the two main damage skills applying their multipliers before defense is subtracted.)
Also, as I mentioned, SaGa games (not counting original SaGa 3, where Thunder is Ice + Tornado, and I don't actually know how this game and Final Fantasy Mystic Quest handle this situation) use the lower defense value of the target, which is more like those newer games you mention. (I also note that there's the occasional weapon art that has a different damage type, like doing blunt damage with a sword, or even electric damage with martial arts.)