The save throws that the OP mentioned are described in detail in the Basic, Expert, and Companion rules (and later condensed in the Rules Cyclopedia.)
- Poison/Death Ray: Your character would make this save throw to avoid instant death. It was the infamous "save or die" mechanic.
- Magic Wands: Your character would use this when trying to jump out of the way of something, such as the beam from a magic wand.
- Paralysis/Turn to Stone: Your character would use this against things that would slow or stop movement, or change their bodies...like a medusa's gaze changing you into stone.
- Dragon's Breath: Your character would use this when trying to cover up from an area effect, like a breath attack.
- Spells/Magic Staff: This was the catch-all save throw for all magical attacks.
In 3rd Edition, these were regrouped into three categories, Fortitude, Reflex, and Will. This was (and remains) my favorite.
In 5th Edition, they were all grouped under different ability scores...and very unevenly, I might add. For every effect or spell that requires a Strength save, there are dozens that require Dexterity or Wisdom. But that rant belongs in another thread.