Are there items or rune sets that would be good to negate or mitigate Karthus' ultimate or any other champions with high burst AP damage?
League-of-legends – How to counter Karthus’ ultimate
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Best Answer
The only complete item-based negation of Karthus' ultimate ability comes from Banshee's Veil and Zhonya's Hourglass. Even Hexdrinker will only mitigate (though, early game, the difference is moot) the damage dealt.
You can successfully mitigate the effects of Karthus' ultimate with items, runes, and masteries geared toward magic resist, however, since it's exclusively magic damage.
Champion abilities such as Nocturne or Sivir's spell shields can negate the effect. Morgana's Black Shield will mitigate the effect. Additionally, Soraka's ultimate, Wish, can mitigate the impact or save an impending death. A properly timed Hallucinate from Shaco (his ultimate), Elise (her Rappel) or Fizz's Playful Trickster can dodge the effects. Essentially, anything that makes you untargetable, when timed correctly, can negate the damage.
A properly timed Waltz of Blades (Fiora's ultimate) or Yi's alpha strike could potentially do it, but timing it would be very tricky. Someone should confirm those last two, however.
Quick Silver Sash will not stop Karthus' ultimate from hitting you. There used to be a glitch where it would remove the red animation, but it wouldn't actually prevent the ability from landing.