Depends on the format, obviously. I'm not sure about anything other than standard, where the fastest kill, as someone on here noted in another topic, is 4 lucky activated archive traps on either the opponent's first turn or yours. Next turn they usually deck themselves
There used to be a way to win on "turn 0" but i dont think it works with some of the rules changes, but i believe you can still do it on your opponents 1st untap step...but im not entirely clear on the rules so dont quote me on that. Just google turn 0 mtg win and it should come up.
If you don't count the possibility of opponent conceding before the game even starts, then Gemstone Caverns+either Spirit Guide+Flash+Protean Hulk is the most reliable 0th turn win for Vintage. To have it Legacy legal, you should have Gemnstone Caverns+Dark Ritual+any black Ritual or Spirit Guide+Entomb+Necromancy. I can't think of a way to win before your own turn in Standard or Extended at the moment.
I actually did something like this in a tournament years ago....my opponent did a t1 channel/fireball combo using the lotus etc...I just removed a Simian Spirit Guide from my hand and cast lightning bolt at him, they were not amused.
^ What AQJ said. Even on your opponent's turn before you go, it is still considered turn 1 in the game. Turn 0 is just a slang term for it.
That being said, the best turn 1 kill in my opinion is Worldgorger. It is the most probable turn 1 kill, doesn't have its main card restricted to 1 like flash for protean hulk decks - as a matter of fact you can have 8 of each card for the combo at least, and only takes 3 mana as far as I know. Not only that, it is black so you have things like Demonic Tutors and Diabolic Tutors for it, Dark Rituals and Cabal Rituals.
In summation.....Star Trek wins a prolonged naval battle against superior, yet less technologically advanced, numbers, with Picard leading the assault, while Kirk takes your soul by laying out Solo and probably his manservant Chewy as well, before impregnating and ditching your Princess.
Fastest is still a type 0 deck. 20 Gemstone Mines and 40 Surging Flames.
Win at next priority and can win in response to anything.
Next up is Flashhulk, which was a real deck in Legacy for a short time.
That doesn't work for a few reasons, firstly, Gemstone Mine cannot in any way give you the 2 mana needed on turn 1 to cast surging flame. Secondly, if you meant Gemstone Cavern, that also doesn't work because it is legendary.
there's actually a topic about this being discussed in the vintage forum. there, we are stacking hands/decks to provide the fastest and most resilient turn 1 wins (turn 0 and turn 1 hard-locks also count) on the play. so far, none of the hands will guarantee victory on the first turn, as there has so far existed an opposing hand that can trip it up or even make it impossible to win. We are using vintage B/R rules (so you can't recall->recall->recall->tendrils).
here are some of our ideas:
The idea behind this one is the same as everyone here has suggested, win as fast as possible while keeping plenty of disruption. Unfortunately, it's not possible for any hand you make to get past both Leyline of the Void and turn 0-1 Trickbind:
Utilizing the 3 mana combo of Shuko+Cephalid Illusionist, once you've milled yourself, there are a number of potential graveyard wins that cannot be disrupted. This unfortunately loses to turn 0-1 Trickbind or Sudden Shock.