My initial reaction upon seeing only one saving throw type in Swords & Wizardry was "huh?".
I couldn't get past the simplicity, it seemed too easy. But then when we test played a session it immediately became clear how elegant only having one saving throw was. Instead of having these discreet, specialized circumstances - it quickly became a measure of will to live, tenacity, and luck - far more common and more useful in a variety of situations!
By thinking of it as a very generalized stat, it became much handier in the game. It also became easier to adjudicate circumstances. In original DnD the categories of saving throws were actually very odd. Why was Death Ray or Poison the same? Why would Wands be different from Staves? And then Dragon Breath seemed very specialized, as did Stone saving throws.
Luck. Will to live. Tenacity. This is how I see the singular saving throw now, and it has greatly improved our gaming sessions. By simplifying, it has actually given us more gameplay.
One thing I am considering is borrowing one of the few innovations in 4th edition I do like, that is making the saving throw a bit like an armor class stat, where the opponent has to overcome it, instead of a number that gets lower with advancement that the victim has to overcome.
For further reading Jeff's Gaming Blog has an excellent series on saving throws well worth checking out.