Abilities that deal bonus damage to turrets
On-hit Effects
Blitzcrank Blitzcrank's Power Fist.png Power Fist
Darius Darius' Crippling Strike.png Crippling Strike
Diana Diana's Moonsilver Blade.png Moonsilver Blade
Ekko Ekko's Phase Dive.png Phase Dive
Gangplank Gangplank's Trial by Fire.png Trial by Fire
Garen Garen's Decisive Strike.png Decisive Strike
Hecarim Hecarim's Devastating Charge.png Devastating Charge
Jayce Jayce's Transform Mercury Hammer.png Transform Mercury Hammer and Hyper Charge.png Hyper Charge
Jhin Jhin's Whisper.png Whisper's 4th shot will still crit structures at 44% reduced damage
Leona Leona's Shield of Daybreak.png Shield of Daybreak
Lucian Lucian's Lightslinger.png Lightslinger
Master Yi Master Yi's Double Strike.png Double Strike
Nasus Nasus' Siphoning Strike.png Siphoning Strike
Nidalee Nidalee's Takedown.png Takedown
Sejuani Sejuani's Flail of the Northern Winds.png Flail of the Northern Winds (only initial blow, not the AoE)
Shyvana Shyvana's Twin Bite.png Twin Bite
Sona Sona's Power Chord.png Power Chord
Talon Talon's Noxian Diplomacy.png Noxian Diplomacy
Twisted Fate Twisted Fate's Pick a Card.png Pick a Card
Vayne Vayne's Tumble.png Tumble
Vi Vi's Excessive Force.png Excessive Force
Volibear Volibear's Rolling Thunder.png Rolling Thunder
Wukong Wukong's Crushing Blow.png Crushing Blow
Xin Zhao Xin Zhao's Three Talon Strike.png Three Talon Strike
Ziggs Ziggs' Short Fuse.png Short Fuse
Area of Effect
Alistar Alistar's Trample.png Trample
Rammus Rammus' Tremors.png Tremors
Sion Sion's Unstoppable Onslaught.png Unstoppable Onslaught
Ziggs Ziggs' Satchel Charge.png Satchel Charge
Targeted
Tristana Tristana's Explosive Charge.png Explosive Charge
Items that deal bonus damage to turrets
Lich Bane item.png Lich Bane
Sheen item.png Sheen
Trinity Force item.png Trinity Force
Iceborn Gauntlet item.png Iceborn Gauntlet
Abilities that are affected when attacking the turret
These abilities are affected when attacking the turret but do not deal extra damage:
Stacking effect
Ashe Ashe's Ranger's Focus.png Ranger's Focus
Draven Draven's Spinning Axe.png Spinning Axe
Graves Graves' True Grit.png True Grit
Jax Jax's Relentless Assault.png Relentless Assault
Nunu Nunu's Visionary.png Visionary
Pantheon Pantheon's Aegis Protection.png Aegis Protection
Volibear Volibear's Frenzy.png Frenzy
Caitlyn Caitlyn's Headshot.png Headshot
Heal
Irelia Irelia's Hiten Style.png Hiten Style
Xin Zhao Xin Zhao's Battle Cry.png Battle Cry
Abilities that affect turrets
Turrets can be shielded by Janna Janna's Eye of the Storm.png Eye of the Storm.
Turrets can be put into stasis by Bard Bard's Tempered Fate.png Tempered Fate.
Last-hitting a turret does not grant bonuses to champions, unless they have a relevant effect:

Twisted Fate Twisted Fate's Loaded Dice.png Loaded Dice grants him from 1 to 6 gold.
Cho'Gath Cho'Gath's Carnivore.png Carnivore restores a small amount of health and mana.
Nasus Nasus' Siphoning Strike.png Siphoning Strike gains permanent damage.
Swain Swain's Carrion Renewal.png Carrion Renewal restores a small amount of mana.

http://leagueoflegends.wikia.com/wiki/Turret

Вот здесь есть все абилки которые работают на турреты.