[RPG] Which Saves oppose which Conditions

In general, you should base the saving throw to be used off of what is causing the effect rather than the effect itself. There are multiple ways to be stunned, some of them require Constitution saves (Monk's Stunning Strike) while others may require Charisma saves (Divine Word). The DMG specifies (pg. 238):

Most of the time, a saving throw comes into play when an effect - such as a spell, monster ability, or trap - calls for it, telling you what kind of saving throw is involved and providing a DC for it.

Other times, a situation arises that clearly calls for a saving throw, especially when a character is subjected to a harmful effect that can't be hedged out by armor or a shield. It's up to you to decide which ability score is involved. The Saving Throws table offers suggestions.

That said, if you don't want to take the time to look up the specific spell or attack causing the effect, or you're in a scenario where a save should occur but the type isn't specified, there is a general rule of thumb.

From the DMG, pg 238:

Saving Throws

• Strength: Opposing a force that would physically move or bind you
• Dexterity: Dodging out of harm's way
• Constitution: Enduring a disease, poison or other hazard that saps vitality
• Intelligence: Disbelieving certain illusions and resisting mental assaults that can be refuted with logic, sharp memory, or both
• Wisdom: Resisting effects that charm, frighten, or otherwise assault your willpower
• Charisma: Withstanding effects, such as possession, that would subsume your personality or hurl you to another plane of existence

The one part here that can be confusing is when to use intelligence and when to use wisdom. The DMG (pg 238) has the following to say about how to determine which to use:

INTELLIGENCE CHECK VS. WISDOM CHECK

If you have trouble deciding whether to call for an Intelligence or a Wisdom check to determine whether a character notices something, think of it in terms of what a very high or low score in those two abilities might mean.

A character with a high Wisdom but low Intelligence is aware of the surroundings but is bad at interpreting what things mean. The character might spot that one section of a wall is clean and dusty compared to the others, but he or she wouldn't necessarily make the deduction that a secret door is there.

In contrast, a character with high Intelligence and low Wisdom is probably oblivious but clever. The character might not spot the clean section of wall but, if asked about it, could immediately deduce why it's clean.

Wisdom checks allow characters to perceive what is around them (the wall is clean here), while Intelligence checks answer why things are that way (there's probably a secret door).