This is a frequently debated point, so I'd like to offer a bit of insight on the ups and downs of various chilling methods. First off, let it be known: the answer will always depend on how much beer one is brewing at a time. Some solutions just aren't cut out for certain volumes. My criteria is simple: what is the least expensive yet still fully effective/efficient method for each size. This always comes down to "how fast is it done" because, well... shoot, unless we want to make an infected beer, this matters! Even if we want an infected beer, it matters for the sake of controlling the infection. Right. Without further ado...
Brewing a "small batch."
By small I mean a few gallons or less. Minus the points on adding water, the next section will suffice very well.
Brewing 5 gallon batches, partial boil.
This means boiling less than the full volume, but usually around 3 gallons or less of boil. For less than 2.5 gallons, using a saline solution with ice in either a bucket or a sink is sufficient, as cool/cold water will still be added into the batch to make the full volume. Even without that step it is likely fine if a bit of external agitation is applied (do not stir unless working in full sterile conditions -- no, you're not).
I do not recommend adding ice, not ever. Simply put: you're going to tend to take on the aromas of the freezer. Perhaps there are ways around this, but the next issue is finding that "right amount." To prepare ice like this, vs doing an ice bath in salt water, then if needed adding cold water doesn't speed the cooling up nor is it more effective in preventing off flavors, so I discourage the practice.
If boiling 3 or more gallons, an argument could be made to step into some equipment as explained on the 5 gallon, full boil section. Rather than argue it, I'll be blunt: the closer you are to 5 gallons of boil, the more time you will save with a chiller. It isn't necessary until you reach "I don't add more than 1/2 gallon of water to my boil when I'm cooling it down." At that point, you're hitting that critical volume where you just aren't going to get it cold as fast as a chiller would using the ice bath.
Brewing 5 gallon batches, full boil.
Use a wort chiller! No, this isn't a joke, mechanical means are required unless you create dry ice routinely (and I'd say that's mechanical up front, so that's still going to count). Immersion chillers are the sensible choice for this size batch. They require little maintenance (hosing them down once done with the cooling is enough), can be made sanitary simply by placing a clean one in the boil about 15 minutes before the end, and are the least expensive option. The added plus that if you think you'll upgrade to a larger brew system, they retain their usefulness as a pre-chiller for tap water in the next options.
Brewing more than 5 gallons, less than 12 (roughly)
This is where the options become "you can go either way." Immersion chillers still work -- provided you bought one big enough. This is something to plan for, a slightly large one is acceptable in smaller batches, but go with one too small and you may retire it sooner in favor of the next options.
- Counterflow Chillers (cfc): a decent cfc will cut down the time it takes to chill your beer drastically. See what I mean here (this gentleman is a customer of our shop and has developed the nicest cfc I've seen so far -- yes, we carry these proudly. The best thing about these devices is that they work on gravity or by being pump-fed. A pump will improve the chilling, but they will work better than immersion without a pump. They are more expensive than immersion chillers.
- Plate chillers: These are always more expensive than any other option, even when that doesn't seem to be so. For example, a great cfc may cost $185, while a plate chiller may run as little as $115. Unfortunately the plate chiller requires a pump, so you're also looking at a $100+ price tag to run it. Also, the smaller plate chillers won't handle much more than 10 gallons as well as the larger ones (Blichmann Engineering's Therminator boasts a confirmed 10 gallons in 5 minutes when using a pump and 55 degree ground water).
Brewing more than 12 gallons
Go with a plate or cfc, or create a mechanical arm / motor unit that may be applied to the pot before end of boil for sterility, for the sake of moving the beer faster through the surface area of the immersion coil. Okay, that's far fetched, but possible and safe if done well. Eventually the counterflow chiller doesn't scale well and requires too much to make it cost-effective, so at a certain volume (I'd argue over 20 gallons) a plate chiller just makes the most sense.
Is there a correct option? No, all have their quirks and requirements. I cannot ever discourage immersion coils -- I still use one for my 10-12 gallon brews. The brewery I'm involved with uses a massive plate chiller, and I wouldn't have it any other way at that scale (unless using a coolship, where applicable, but that's not something we're doing at the brewery).
That's not the real conclusion; the real conclusion is up to you. Now for some humor and "don't ever do this." These are things people try that I must stress can go very wrong.
- Using a snowbank. This is perhaps the slowest method. The logic is "I'll put the pot into the snow, snow is cold, it'll make it cold!" Well, sure, but it will melt the snow. This creates space, that space is filled with hot air.... insulation becomes the theme. "But I can load that space with snow as it melts!" Yes, and by the time you've chilled the beer down, you could have brewed another batch. This is not a joke. Don't try this, 3 hours is the average cooldown time.
- I'll just put it in the fridge. You know that this is a bad idea, deep down, but I'll explain why: you're going to damage more than just your beer. Half-cooking the food that is near; the massive temperature change bringing loads of humidity into the fridge; smaller levels of thermal exchange means you're still not going to chill it fast enough... Oh, just don't. Please. There isn't sufficient thermal conductivity, for the technical answer.
- I'll drop Ice into my partial boil. Hey! Didn't we already cover this?
- I'll stick it outside overnight, it'll be good by morning. This actually could work. The real point of so much of what we do when brewing is to MINIMIZE risk of things going wrong. This is the opposite, it is asking for trouble. Might work well enough though. If this appeals, you might want to consider being a sour beer brewer.
Missing a few good or bad ideas? Sure. Hopefully you feel confident in making a choice that suits you but, as always, ask if you want more information!