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?
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.
The best way is Silence/Taunt/knock back/Kill Karthus, before he finish his ultimate. But if that is not possible, here a list of items and champions that have the anti-karthus mojo.
Places your champion into stasis for 2 seconds, rendering you invulnerable and untargetable but unable to take any actions.
Blocks one negative spell every 45 seconds.
If you would take magic damage which would leave you at less than 30% of your maximum health, You gain a shield which absorbs up to 250 magic damage
Maw of Malmortius:
If you would take magic damage which would leave you at less than 30% of your maximum health, you first gain a shield which absorbs up to 400 magic damage
Incoming magic damage is multiplied by a factor based on the unit's magic resistance:
- Shaco's Hallucinate (Active): Shaco stealths for half a second and creates a clone of himself next to him... (When used in the right moment can avoid it)
- Sivir's Spell Shield (Active): Creates a magical barrier that lasts up to 3 seconds which blocks a single enemy ability used on Sivir. If an ability is blocked by the shield, Sivir regains 150 mana.
- Nocturne's Shroud of Darkness (Active): Nocturne creates a magical shield for 2 seconds which can block the next enemy spell that hits him.
- Kayle's Intervention (Active): Kayle bathes a target ally champion (or herself) in holy light, rendering them immune to all damage for a few seconds.
- Akali's Twilight Shroud (Active): Akali throws down a circular cover of smoke that lasts for 8 seconds. While inside the area, Akali gains armor and magic resistance
- Janna's Eye Of The Storm (Active): Janna conjures a defensive gale that shields her target from incoming damage for up to 5 seconds.
- Morgana's Black Shield (Active): Places a shield around target friendly champion, absorbing magic damage and preventing disables while the shield holds.
- Blitz's Mana Barrier (Innate): When Blitzcrank's life is brought below 20% health he activates Mana Barrier, creating a damage shield that lasts 10 seconds. The shield strength is equal to 50% of Blitzcrank's current mana
- Lux's Prismatic Barrier (Active): Lux shields herself for up to 3 seconds and throws out her wand to a target location
- Malphite's Granite Shield Malphite's skin innately produces a layer of rock as a shield which absorbs damage of up to 10% of his maximum health.
You can choose to stun, knockback/up, silence Karthus, which cancels his ult (unless he is in his resurrected mode).
You can build: Banshee's Veil which blocks 1 spell every 45 seconds.
Hexdrinker which blocks 250 Magic Damage when you go under 30% hp every 60 seconds.
Maw of Malmortius blocks 400 damage instead of 250 damage and is built from Hexdrinker.
Magic Resist, additional health makes it so Karthus' ult does less damage to your total health.
Fizz use his E to become untargetable which makes it so Karthus' ult doesn't hit him.
Vlad's W makes him turn into a pool, making it so Karthus' ult doesn't hit him.
Shields can absorb the magic damage that Karthus' ult does.
Tryndamere's ult prevents him from dying for a short duration, so you can use that if Karthus' ult threatens your existence.
Morgana's E is a shield which blocks a certain amount of magic damage.
Kassadin's Q interrupts any channelled spell, including Karthus' ult.
Magic Resist can stop some of the damage, and there are other shielding item that can stifle the damage such as Locket of the Iron Solari. Also, since Requiem is a channeled spell, assuming that Karthus isn't in his Ghost form, you can hard CC him and he won't finish using it. If you're trying to counter-pick Karthus, Soraka's Wish could work or you can pick a champion that uses a Spell Shield like Nocturne or Sivir. To stifle the damage, any shield will work such as Rumble's Scrap Shield or in the case of Requiem's magic damage you could use Morgana's Black Shield.
yes, there are a few things you can do to counter karthus' ultimate. if he does it when alive, kill him or silence him and it will stop casting. or build a banshees veil under the magic resist tab, as it stops one spell every 45 seconds from hitting you. the hexdrinker also absorbs magic damage. Or just building health or magic resist based on what champion you are playing so that it doesn't have to hit you that hard.
Be aware of the timing once its used, since Requiem has a long cooldown even with CDR. While its up, allow for that much hp as your minimum, instead of engaging with very low health without going back to heal. Also be more generous with pots - its not fun to die because you tried to save a 35g health potion.
As always, you need MR when looking to mitigate magic damage, some items to get depending on your role:
ADC: Hexdrinker / Maw of Malmortius
APC: Lich Bane, Zhonya's Hourglass
Any: Banshee Veil (more useful on mana casters, and esp. if other team also has strong stun/snare skills)
Simply increasing HP is also an option; tanks like Shen can just grab Warmog's as usual for an hp buffer.
Shields or going untargetable will help counter or avoid the damage on a per champion basis. Soraka's Wish mitigates it for entire team (except people on full hp, who won't die from the requiem).
If your team is close together (team fights etc.), you can heal with Janna's ultimate or shield using Locket of the Iron Solari.