I've heard of many different methods of chilling wort, What is the fastest? And what's the best cost vs speed solution?
Plate chillers are generally regarded as being the most efficient, and so typically require less water for the same amount of cooling compared to counter flow and immersion chillers.
The largest plate chillers from dudadiesel can chill a 10 gallon batch in 15 seconds according to their figures, but these cost over a grand, and they are using flowrates not easily achievable at home. The smaller, more reasonably priced chillers (around $100) can do the job in 5-8 minutes.
Adding liquid helium to the kettle would probably be pretty fast, but not exactly practical. For home use I guess a beefy plate chiller would be the fastest alternative, but those can be expensive. A basic stainless steel or copper immersion chiller can be very reasonable and will chill your wort plenty fast. As long as you reach pitching temperature within 20-30 minutes you are more than good to go.
Dump it on a large/flat/cold surface.
Since evaporation is the quickest way to cool such a liquid, and maximizing surface area maximizes evaporation, this is the optimal answer I can come up with. Given enough cold area, this should chill the liquid in much less than a second.
The cost would depend on many factors.
As for price vs speed: The cheapest would be to not do anything with it. Just allow thermodynamics slowly bring it to equilibrium with it's environment. This is actually what I would do since it's the cheapest, simplest, and laziest solution.
I gravity feed a Therminator chiller from my boil kettle. With my faucet turned on halfway, I get 65 degree wort from boiling with one pass. It takes about 5 minutes to drain 5 gallons into my carboy. I don't think you can reasonably ask for better than that.
The Therminators retail for around $200.
I tried a DudaDiesel plate chiller and was totally unsuccessful. Went back to a large copper immersion chiller. I frequently chill 9-10 gallon batches in about 18 minutes. And I use virtually all of the excess water to clean my 3 15 gallon kettles.
FYI - I have a barely used plate chiller that I will sell cheap!
To add to what Jeremy said, I use the smaller Shirron plate chiller, which is about half the thickness and half the price of the Blichmann Therminator, and it also works fabulously. I generally have the water on full, so I'm probably using twice as much water for the same results, but otherwise my speed and temperature numbers correspond to what Jeremy reports. It's an excellent investment, will save you a lot of time, and it's not all that much more expensive than many immersion chillers.
That said, if saving money is your top concern, depending on the size of your boil kettle, you may be able to set the whole thing into a utility sink or large tub filled with ice water.