For reference, as of The Circle Undone, here is a list of negative effects that Eldritch Inspiration can be used to mitigate:
Alchemical Transmutation - Take 1 damage.
Astral Travel - Discard an item or ally asset from play, take 1 damage if you cannot.
Blinding Light - Lose 1 action.
Blinding Light (2) - Lose 1 action and take 1 horror.
Mists of R'lyeh & Mists of R'lyeh (2) - Choose and discard a card.
Recharge (2) - Discard the chosen asset. (Note: You still don't get the 3 charges in this case.)
Rite of Seeking & Rite of Seeking (2) & Rite of Seeking (4) - Lose all remaining actions and end your turn.
Seal of the Seventh Sign (5) - Remove 1 charge from Seal of the Seventh Sign.
Shrivelling & Shrivelling (3) - Take 1 horror.
Shrivelling (5) - Take 2 horror.
Storm of Spirits - Deal 1 damage to each investigator at your location.
The Chthonian Stone - Return The Cthonian Stone to your hand.
Here is a list of positive effects that can be doubled using Eldritch Inspiration:
Eldritch Inspiration - Can actually be used on a second copy of itself, but it won't quadruple the effect it will just triple it.
Hypnotic Gaze - Deal an attacking enemy's damage to itself.
Jewel of Aureolus (2) - Draw a card or gain 2 resources.
Recall the Future (2) - +2 skill value for this test (named , , , or token only).
Ritual Candles - +1 skill value for this test.
Song of the Dead (2) - +2 damage ( only).
Note that and on cards will count as triggers for this card, as per the Rules Reference. Father Mateo doesn't actually get an additional benefit from repeating his conversion of to , and Jim Culver's to 0 conversion is static and not a trigger.