MTG Salvation

One possibility is to hit double Virulent Sliver, one of the haste slivers and some other components, and deal 10 poison on turn three.

Turn one:
Forest
Virulent Sliver

Turn two:
Second Virulent Sliver
Attack for 2 poison
Land
Any 1-drop sliver (eg Gemhide Sliver)

Turn three:
Land
Any hastey sliver (eg Heart Sliver)
Attack for 8 poison
gg

Any other theoretical turn three wins you can come up with?
There was a thread with a turn 2 win, but that seems rarer.

Turn one:
Mountain
Faithless Looting, discarding Dragon Breath and Ulamog's Crusher

Turn 2:
Swamp
Exhume Crusher, which triggers Dragon's Breath
Attack for 8, annihilate 2

Turn 3:
Mountain
Bolt their blocker (optional)
Attack for 8, annihilate 2
Fling Crusher for 8 more

A turn two Kiln Fiend backed by either Assault Strobe or Temur Battle Rage can come in for 20 in lots of different ways on turn three. Lightning Bolt is useful for bringing an opponent in range when they play the lifegaining duals, and Apostle's Blessing, Artful Dodge and Shadow Rift can all get the Kiln Fiend past blockers.

Gitaxian Probe could go in that deck as well, just pay 0 mana to pump and draw a card.

Or Manamorphose.

Turn one:
Mountain
Faithless Looting, discarding Dragon Breath and Ulamog's Crusher

Turn 2:
Swamp
Exhume Crusher, which triggers Dragon's Breath
Attack for 8, annihilate 2

Turn 3:
Mountain
Bolt their blocker (optional)
Attack for 8, annihilate 2
Fling Crusher for 8 more

Instead of crusher, you could use Chained Throatseeker 5-power infect and not have to fling. [EDIT: Wait, it can't attack yet.]

Or give Ulamog's Crusher a Phyresis [EDIT: or Tainted Strike] for infect on turn three, and use Mutagenic growth or Giant Growth etc for 10 poison. You don't even need to give it haste.
[EDIT AGAIN: This is theoretical turn 2 win with Dragon Breath. - no it isn't]
[EDIT SOME MORE: More creatures are Eldrazi Devastator and Ancient Brontodon.]

Mountain, Rite of Flame, Rite of Flame, Immolating Souleater, Reckless Charge, Assault Strobe, activate Souleater 6 times, attack for 20

Plains, Tireless Tribe
Island, Inside Out, discard 5 cards, attack for 21

Forest, Glistener Elf
Forest, Groundswell, Giant Growth, Mutagenic Growth, attack for 10 poison

Plains, Lotus Petal, Lotus Petal, Skyhunter Skirmisher
Plains, Ethereal Armor, Ethereal Armor, attack for 10
Attack for 10

Island, Delver of Secrets
Delver transforms somehow, Island, Lotus Petal, Unstable Mutation, Unstable Mutation, Unstable Mutation, attack for 12
Attack for 9

Swamp, Dark Ritual, Beckon Apparition, Edge of the Divinity, Edge of the Divinity
Edge of the Divinity, attack for 10
Attack for 10

Mountain, Rift Bolt
Mountain, Flame Rift
Mountain, Lava Spike, Chain Lightning, Shard Volley, Fireblast

Mountain, Foundry Street Denizen
Mountain, Burning-Tree Emissary, Burning-Tree Emissary, Keldon Marauders (deal 1), attack for 4
Goblin Bushwhacker with kicker, attack for 15

Plains, Steppe Lynx
Plains, Steppe Lynx, Steppe Lynx, attack for 2
Forest, Harrow or Crop Rotation for Evolving Wilds, attack for 18

Swamp, Grasping Scoundrel
Forest, Putrid Leech, attack for 2
Forest, Groundswell on Putrid Leech, Activate Putrid Leech, attack for 10, Rite of Consumption for 8

Great Furnace, Kuldotha Rebirth
Attack for 3
Mountain, Rites of Initiation discarding 5 cards, attack for 18

Many of the cards are interchangeable—Putrid Leech or Keldon Marauders could be Wild Mongrel, for example. Pump, damage doubling, and mana cheats are all good for theoretical kills because they trade stability for power. This Balustrade Spy deck can kill on turn 1, but I don't recall how it works.

Based on your post, Black_Cockatoo:
Island, Careful Study discarding Ancient Brontodon and Dragon Breath, Lotus Petal, Dark Ritual, Exhume, Tainted Strike, attack for 10 poison

Swamp, Dark Ritual, Putrid Imp, discard Ancient Brontodon, Exhume
Tainted Strike on Brontodon, attack for 10 poison

Amazing post. Turn-1 wins in pauper make it sound like it would be degenerate.

Swamp, Dark Ritual, Putrid Imp, discard Ancient Brontodon, Exhume
Tainted Strike on Brontodon, attack for 10 poison

All you need is a Lotus Petal or Simian Spirit Guide and a Dragon Breath to make this a turn-oner like the previous.

Should totally build this deck when I have extra cash.

Something like this or a build with Dark Ritual and Putrid Imp. I took out poison because I ran out of cards, but that could easily go in somewhere as well.

This mono-black build feels alright. It needs to be tested against the field, of course.