1e and 2e
Saves were based on class and level only and broken into 5 categories, as you gained level effects were more difficult to affect you. So as those save or die effects came on board, your saves were much better and made them much less likely to affect you. So single variable based on defenders level.
There was also Magic Resistance expressed as a percentage, in 1e there was a complex % modification based on the level differences. In 2e the % was static and could not be changed. Single variable.
3e
Saves were based on class, level, and stats. Also only 3 saves based on 3 stats. Then DCs were generally 10 + 1/2 level + stat, or 10 + spell level + stat. So lots of variables. The net goal though was to make the bonuses and DCs stay relatively in the same ball park. This system did have some notable problems muticlassing save bonus stacking, spellcaster's ability to get DCs out of the range of the defender to make a save.
You also had Spell Resistance which replaced the Magic Resistance rules. The subsystem was basically a caster level check against a DC, the more powerful the monster or effect that granted the SR the higher the DC. So two variables.
4e
Saves were flipped on there head and no longer were something that you made a roll on, but became like an Armor Class score. Now the attacker rolled to hit you and the defender set the DC. The math remained the same as in 3e however was streamlined to +1/2 level on both the attackers end and defenders end. This also had a major problem, stat polarity. Saves were generated from, the highest of two stats. So in effect characters were designed to pump one stat and dump the other stat. Another problem is that the iconic "I failed my save" term was lost, due to the attacker rolling to hit their opponent with their powers.
It has been been a while since I have played 4e, but I think SR was removed. This is a good choice imho.
5e
Saves in 5e are based on all 6 stats, remove the +1/2 level, and go back to having the defender roll them. They are stat checks vs a DC that is 10+stat. I favor this system the best, likely because this is something I proposed in the way back. LOL.
One potential issue I see, is that in 1e and 2e, saves of higher level characters got much better, so as more powerful effects came the character's save was better equipped to deal with them. He could resist finger of death at a higher clip. 3e took a detour from this concept, which used a very similar spell system as 1e/2e but more powerful effects were couple with more difficult to resist higher DCs. High level spellcasters became even that much more potent.
The system as presented in the 5e playtest keeps the higher level DCs flat (another thing I proposed in the way back) with the lower level spells. So the DC of a first level spell is the same DC of a 9th level spell. Again the effect is much more powerful, why double down with a higher DC too.
So my concern is that characters should get better at saving throws as they level up like in 1e/2e to combat the higher level effects. I like the 1e/2e method of savings throws. I also really like the flat DCs and save modifiers. This does fly in the face of another concept that I like about the currently drafted 5e save rules though. I like that a 20th level fighter has the same chance of getting drunk as a 1st level fighter. Both have the same chance of failing their save (barring magic items and stat boosts to the 20th level fighter).
I like the saves based on all 6 stats. However, with this regard some work needs to be done on clearly delineating the mental saves. INT is figuring things out. In 1e/2e a high INT made you immune to illusions, illusions should be based on INT saves. If perception is synonymous wisdom, wisdom should only provide perception like saves ("surprise" save for instance) and if CHA is your force of personality, this should be your willpower. This will allow you to resist mind control and stuff like that. The other new save is STR and this is an easy save to delineate, resist grapples, resist getting knocked down, resist letting go of the rope when it is yanked etc.
One last stride is the removal of SR/MR from the game, this is a secondary save mechanic that really added a lot of complexity and not a lot of value. Want to make golems immune to magic just give them a trait that says immune to direct magical effects.
All in all, I think the direction is very good.
So what was your favorite edition for saves and why?