I don't know the exact history of the saving throw mechanic across the various editions of D&D and its ilk. I do know that it has changed considerably in detail, but not in essence — regardless of the specific implementation, it gives the player a chance to avoid or ameliorate some sort of effect, be it damaging or not.
AD&D has a fairly byzantine system, in which saving throws are split into categories depending on the effect. Some effects, however, fall into two or more of those categories, and as far as I'm aware it has never been unambiguously stated how those categories were originally conceived. The Rod Staff or Wand category, for example, would seem to embrace the agility needed to avoid the magical rays cast from them, but the trouble is that the effects created by rods, staffs, and wands are by no means limited to dodgeable rays.
The categories, in order, are
- Paralyzation, Poison, or Death Magic
- Rod, Staff, or Wand
- Petrification or Polymorph
- Breath Weapon
- Spell
I've read opinions that this is supposed to be read as a hierarchy of effects, but the arguments are not compelling.
Like the concept of hit-points, AD&D saving throws are pretty abstract. The exact way they work isn't really spelled out, and is left largely to the imagination.
D&D3e introduced a three category saving throw system:
- Fortitude
- Reflex
- Will
They were based on the character's abilities: CON, DEX and WIS respectively, and instead of basing the saving throw on a class of effects, the important thing is to decide how the attack would affect the character and assign a save category accordingly.
The character's level is still the most important influence on the likelihood of making or failing a save, but now (some of) their characteristic totals also become relevant.
One side-effect of the change to this system is that saving throws become a bit less abstract, and there's no implicit mechanism to reflect pure luck. How does a warrior, pinned spreadeagled to a rock wall, save vs. the breath of the dragon who is about to incinerate them? None of the characteristic-based saving throw categories would really apply without an unconscionable amount of hand-waving.
I know little of D&D4e, and what I did see of it I hated. let us pass it by.
D&D5e ties saving throws even more closely to the character's ability scores, and now they're implicitly a STR save, or a CON save, or an INT save, or whatever. On the face of it, it's a simple, logical system, and for the most part it works fine. Just like D&D3e, the effect on the character and the nature of the attack are the most relevant things, and just because an attack comes from a wand, there's nothing specifically wand-ish to be considered when determining which characteristic to save against.
D&D5e reduces the abstraction of the saving throw mechanic even further than D&D3e, and again, there's no specific method of reflecting a save based purely on luck.
The saving throw mechanic used by the Swords & Wizardry retroclone simplifies matters considerably. Each character class has a single Saving Throw target number. There's no worrying about the nature of the effect, or the character's abilities, or any of that. A saving throw is just a saving throw; it'll always be the same at any given level regardless of how or why a save is required.
Fighters have the worst saves (though not by much). Wizards are better. Thieves have the best saves (though not by much). As with other variants of D&D, the saving throw target number gets lower as the character rises in level, but there's just the one target number at any given level.
Having a single save is also advantageous if one wants to go the characteristic save route, as used in D&D5e, since you can just add (or subtract) any ability modifier to (or from) the target number, and Bob's your uncle. In S&W that's unlikely to make much of a difference; as it's a 0D&D retroclone, ability modifiers tend to be small.
This is the most highly abstracted, and in my view the most elegant, saving throw system within the extended D&D fold, and I like it very much. It performs the basic function of the saving throw (allowing the character to escape some or all of an effect) but it is not tied to anything but the character's level. Want to avoid some falling damage? Make a saving throw. Being attacked by an acid-spitting dong-worm? Make a saving throw. Want to remember something your character knows but you can't recall? Just make a saving throw. Easy-peasy. How did the save work? I dunno, make it up. These games are supposed to be games of imagination.