Well, I think the title is pretty much self-explanatory. I've seen a lot of people ask in the forums or around the web 'What type of damage does this ability do?', and even though the information is available in the Learning Center (http://www.leagueoflegends.com/champions), there's no 'at a glance' list with just the basics.
Therefore, I decided to make one and below you will find all the Champions in League of Legends (as of today, September 14), along with their offensive abilities (there are some exceptions I felt noteworthy to include though) and, most importantly, their damage types.
I emphasized offensive abilities because even though Tryndamere for instance only has Spinning Slash as a magical damage ability, this doesn't mean that he's a mage (I think that big-ass sword of his is a dead giveaway).
I hope you will find this list useful and feel free to poke me if there is something that should be added or if there are any mistakes.
Akali

Aug 19, 2014  Drag the 'League of Legends' application into the 'Applications' folder. Unmount the DMG file from finder again. Go to your applications folder and run League of Legends directly from there. League of legends can't run from the dmg.

• What Kind Of Dmg Does Ornn Do League Of America
• What Kind Of Dmg Does Ornn Do League Work
• What Kind Of Dmg Does Ornn Do League Work
• What Kind Of Dmg Does Ornn Do League Table

1. Ornn's W was his main ability, for all kind's of things, tanking dmg, going aggro on someone, trading, escaping from enemies, dodging stuff while rooted, etc. Some things out of there he still does, others he doesn't, Ornn no longer tanks dmg, his shield did that for him and now there is no shield.
2. Ornn gains additional armor and magic resist from all sources. He also can purchase items from anywhere on the map. Once he reaches level 12 any item that is a masterwork item that Ornn owns or purchases is upgraded for free. For each level after level 12.

Aug 18, 2017  Ornn will make an effective Support due to his build path which focuses on CDR and tankiness, and his kit that stays relevant due to its usefulness regardless of damage. In lane, he’ll be quite versatile as far as play style since he can use his Q as a useful. Ornn can spend gold to forge non-consumable items anywhere. Additionally, when Ornn reaches level @MasterworkLevel@, he will upgrade any eligible items into masterwork items for himself, up to 2 max. For each level after @MasterworkLevel@, Ornn can upgrade an item for an ally by going near them and clicking on them, max 1 per ally. Ornn slams the ground, sending out a fissure that deals physical damage and slows enemies. After a small delay, a magma pillar forms at the target location, functioning like a tiny wall for a few seconds. Physical Damage. General Counter Tips. If his W is on cd try to all in on him Report. How to counter Ornn as Tahm Kench. No tips found. Be the first to submit a counter tip! Click the Tips button to view more or to submit a tip! Edit Gold is only deducted upon completing the channel. The reduction in Tenacity will benefit all applicable types of crowd control, not just immobilizes. Effects such as slows, blinds and silences will be empowered without consuming the debuff. Despite the in-game tooltip attribute Brittle to Bellows Breath, it is not required to rank Bellows Breath in order to benefit from the effect.

• Mark of the Assassin - Magic
• Crescent Slash - Physical
• Shadow Dance - Magic

• Pulverize - Magic
• Headbutt - Magic

• Bandage Toss - Magic
• Despair - Magic
• Tantrum - Magic
• Curse of the Sad Mummy - Magic

• Flash Frost - Magic
• Frostbite - Magic
• Glacial Storm - Magic

• Disintegrate - Magic
• Incinerate - Magic
• Molten Shield - Magic
• Tibbers - Magic

• Volley - Physical
• Enchanted Crystal Arrow - Magic

• Rocket Grab - Magic
• Power Fist - Physical
• Static Field - Magic

• Rupture - Magic
• Feral Scream - Magic
• Vorpal Spikes - Magic
• Feast - True Damage -> Ignores Magic Resist

• Phosphorus Bomb - Magic
• Valkyrie - Magic
• Gatling Gun - Physical
• Missile Barrage - Magic

• Infected Cleaver - Magic
• Burning Agony - Magic
• Masochism - Increases physical damage

• Hate Spike - Magic
• Ravage - Magic

• Mystic Shot - Physical
• Essence Flux - Magic
• Arcane Shift - Magic
• Trueshot Barrage - Magic

• Drain - Magic
• Dark Wind - Magic
• Crowstorm - Magic

• Resolute Smite - Magic
• Righteous Gust - Magic
• Idol of Durand - Magic

• Parrrley - Physical
• Cannon Barrage - Magic

• Decisive Strike - Physical
• Judgment - Physical
• Demacian Justice - Magic

• Barrel Roll - Magic
• Drunken Rage - Increases physical damage
• Body Slam - Magic
• Explosive Cask - Magic

• H-28G Evolution Turret - Magic
• Hextech Micro-Rockets - Magic
• CH-1 Concussion Grenade - Magic

• Howling Gale - Magic
• Zephyr - Magic

• Leap Strike - Magic
• Empower - Magic
• Counter Strike - Magic
• Relentless Assault - Magic

• Lay Waste - Magic
• Defile - Magic
• Requiem - Magic

• Null Sphere - Magic
• Force Pulse - Magic
• Riftwalk - Magic

• Bouncing Blade - Magic
• Shunpo - Magic
• Death Lotus - Magic

• Reckoning - Magic
• Righteous Fury - Magic

• Thundering Shuriken - Magic
• Electrical Surge - Magic
• Lightning Rush - Magic
• Slicing Maelstrom - Magic

• Caustic Spittle - Magic
• Bio-Arcane Barrage - Magic
• Void Ooze - Magic
• Living Artillery - Magic

• Seismic Shard - Magic
• Brutal Strikes - Unknown, increases damage for 6 seconds
• Ground Slam - Magic
• Unstoppable Force - Magic

• Call of the Void - Magic
• Null Zone - Magic
• Malefic Visions - Magic
• Nether Grasp - Magic

• Alpha Strike - Magic
• Wuju Style - Increases physical damage

• Mace of Spades - Magic
• Creeping Death - Magic
• Siphon of Destruction - Magic
• Children of the Grave - Magic

• Dark Binding - Magic
• Tormented Soil - Magic
• Soul Shackles - Magic

• Siphoning Strike - Physical
• Spirit Fire - Magic
• Fury of the Sands - Magic

• Javelin Toss / Takedown - Magic
• Bushwhack / Pounce - Magic

• Ice Blast - Magic
• Absolute Zero - Magic

• Undertow - Magic
• Reckless Swing - True damage

• Spear Shot - Physical
• Aegis of Zeonia - Magic
• Heartseeker Strike - Physical
• Grand Skyfall - Magic

• Devastating Blow - Magic damage
• Heroic Charge - Magic

• Powerball - Magic
• Defensive Ball Curl - Magic
• Tremors - Magic

• Overload - Magic
• Rune Prison - Magic
• Spell Flux - Magic

• Deceive - Physical
• Jack In The Box - Magic
• Two-Shiv Poison - Magic
• Hallucinate - Magic

• Vorpal Blade - Magic

What Kind Of Dmg Does Ornn Do League Of America

• Poison Trail - Magic
• Fling - Magic

• Cryptic Gaze - Magic
• Death's Caress - Magic
• Enrage - Increases damage

• Boomerang Blade - Magic

• Starcall - Magic
• Infuse - Magic

• Shatter - Magic
• Dazzle - Magic

• Blinding Dart - Magic
• Toxic Shot - Magic
• Noxious Trap - Magic

• Rocket Jump - Magic
• Explosive Shot - Magic
• Buster Shot - Magic

What Kind Of Dmg Does Ornn Do League Work

• Spinning Slash - Magic

What Kind Of Dmg Does Ornn Do League Work

• Wild Cards - Magic
• Pick A Card - Magic
• Stacked Deck - Magic

• Expunge - Magic
• Spray and Pray - Unknown (Physical, in theory)

• Tiger Stance - Magic
• Phoenix Stance - Magic

• Baleful Strike - Magic
• Dark Matter - Magic
• Primordial Burst - Magic

• Transfusion - Magic
• Sanguine Pool - Magic
• Tides of Blood - Magic
• Hemoplague - Magic

• Hungering Strike - Unknown (Magic, in theory)
• Infinite Duress - Unknown (Physical, in theory)

• Three Talon Strike - Physical
• Audacious Charge - Magic
• Crescent Sweep - Physical

What Kind Of Dmg Does Ornn Do League Table

• Time Bomb - Magic