There are five basic conversion techniques I'm aware of:
1. Channel Mixer
2. Black & White
3. Hue/Saturation
4. Gradient Map
5. ACR Greyscale
These adjustment layers do not, all by themselves, necessarily constitute a complete greyscale conversion workflow, but they do form the basis for such a workflow. Other steps in the workflow can include just about anything including curves, dodge/burn, and localized editing.
Anyway, whenever I hear about a method for converting from color to black and white, my first question is always, "How does this method relate to a standard luminosity conversion".
What I mean by "standard luminosity" conversion, I mean a black and white image where the brightness value of each B&W pixel is calculated from the luminosity of the original color pixel. The formula for luminosity is:
Luminosity = 0.30 x Red + 0.59 x Green + 0.11 x Blue.
In other words, the value of grey in the black and white image will be calculated from the three primary color values as shown in that formula.
This formula roughly corresponds to how the human eye responds to the three primary colors. Ie., we see blue as an inherently dark color (only 0.11 weighting factor) because our eyes are less sensitive to it. We see green as a bright color (0.59 weighting factor). Red is in-between. I consider this as the most "normal" type of B&W conversion and I like to get my bearings relative to this setting. Understanding how each B&W method relates to luminosity is helpful in understanding the operation of those tools--at least from a technical standpoint. It's also important when you start to use these methods to manipulate the luminosity of a color image (not dicussed here.)
For what it's worth, I believe luminosity is a Photoshop-specific concept. The more "official" term is luminance. The formula for luminance is very similar to, but not quite the same as luminosity:
Luminance = 0.21 x Red + 0.72 x Green + 0.07 x Blue
Luminance puts even more weight into green and less into red and blue. In practice, there's hardly any visible difference between them and since Photoshop is all geared towards luminosity, that's what I've standardized on.
Channel Mixer
Let's start with the channel mixer because you can enter the factors from the luminosity formula directly. To get luminosity greyscale, create a channel mixer adjustment layer, check the monochrome box, then enter the values 30, 59, 11 into the R,G,B source channels as shown. This is essentially doing what we said with the formula above--take 30% of red, 59% of green, and 11% of blue, add them up, and that's the grey value in our B&W image.
I can now try other combinations and feel like I know what's going on because I started from a known reference point--ie., luminosity. For instance, a red filter would be equivalent to turning the green and blue components down to zero (or almost zero) and turning red up. This is a popular combination because it makes blue skies very dark and gives clouds a lot of contrast. To keep things correctly exposed, you generally want the three RGB values to add up to about 100. Depending on how much you want to preserve highlights or shadows in your B&W image, you might vary from this, but it's a good rule-of-thumb. Anyway, you get the idea.
The channel mixer operates on the primary colors of an image--it doesn't care about the source color saturation. For example, turning down the blue slider will darken a blue sky, but it'll at least partly darken any pixel that contains any blue at all--even a white or a grey pixel will get darker because the blue primary gets turned down. Of course you also are just working with three sliders, so if you want to darken, say, purple without darkening blue, you really can't do that terribly well. But for most situations, juggling the sliders around will get a good result. For reference, I think Photoshop might already ship with a luminosity preset for the channel mixer.
Here's an example just to give you a visual. The original is shown, followed by the "standard" luminosity conversion (30,59,11), followed by an extreme yellow filter (red and green boosted, blue turned way down--negative in this case).
Black and White Layer
Next I want to look at the Black&White adjustment tool (CS3 and later). This tool treats an image as though it's comprised of six primary colors instead of three: red, yellow, green, cyan, blue, and magenta.
How do we create the "normal" luminosity B&W conversion with this thing? Well, for starters, you enter in the same values for R, G, and B you did in the channel mixer: 30, 59, and 11 respectively.
Remember how the additive primaries (RGB) relate to the subtractive primaries (YCM)? Here's the relationship:
Yellow = Red + Green
Cyan = Green + Blue
Magenta = Blue + Red
If we do that in the B&W tool, the values to enter for Y,C, and M are: 89, 70, and 41 respectively as shown below:
And this becomes our "normal" B&W conversion using the B&W adjustment layer in photoshop. It gives exactly the same result as the 30,59,11 combination using the channel mixer. Again, starting from this point, I can experiment with artistic variations on my definition of normal and I prefer this to the Photoshop default. Again, I have a preset in my B&W adjustment layer called "luminosity" that I always load first before continuing with adjustments.
Unlike the Channel Mixer, the sliders in this layer only operate on pixels with that color in them. So using our example of turning down blue, turning down the blue slider here will also darken a blue sky, but it won't alter any of the other colors even if they contain a small amount of blue primary. It also will have no effect on pixels that are already grey. In that regard, this method is more intuitive. It's also more selective because it only effects the colors of the sliders and there are six sliders instead of only three in the channel mixer.
Another comparison is in order. I repeated (roughly) an extreme yellow filter in the B&W tool. You can see the settings for each adjustment layer. The yellow filter is much more straightforward for the B&W layer--you just turn up yellow and turn down blue. It was much quicker to obtain this result because I wasn't adjusting and readjusting the sliders as was needed in the channel mixer. And if I'd wanted I could adjust reds independently--this would be a lot more laborious (if not impossible) with the channel mixer.
Notice also that the B&W tool blue slider is turned all the way down--it's out of steam. The channel mixer still has a lot of adjustment range leftover. This is a good illustration of the fact that while the channel mixer may be less intuitive, it's capable of quite extreme adjustments. Of course you can always combine either with further adjustments such as curves or local adjustments to get more extreme results as well.
Hue/Saturation
Now what about the hue/saturation (aka H/S/L) adjustment layer? If I add an H/S/L layer and turn the saturation slider all the way down, I get a greyscale image as well. It's fairly normal, but it's not luminosity. That's because the definition of "L" (lightness) used by this layer follows the formula:
Lightness = 1/2 x (max + min)
In other words, to get the greyscale value, add the maximum of R,G,B and the minimum of R,G,B and divide the result by 2. If you've ever read about the HSL color space, this is where that comes from. I'm no color expert, but I think the HSL color space might be more useful for graphic artists than for photographers. No amount of adjusting can get an HSL greyscale image to be the same as luminosity.
So comparing Lightness to Luminosity. If I had a color of RGB = 250, 44, 88, the luminosity greyscale value would be 250x0.3 + 44x0.59 + 88x0.11 = 111. The lightness greyscale value would be 0.5 x (250 + 44) = 147. Such greyscale conversions look okay, but it's not luminosity and thus may give subjectively unpredictable results.
You can also mess around with the lightness (not luminosity) of colors in much the same way as we did with the B&W tool. Not only that, you have complete control over exactly which color ranges you are adjusting (unlike the B&W tool which is at fixed hues). However, the range of adjustment is miniscule compared to the previous two methods.
Here's a comparison of our yellow filter example again. As shown, I had to make three adjustments to the H/S/L layer. First, I turned saturation all the way down. Next, select the yellows and turn the lightness all the way up. I also adjusted the range of yellows in the bottom hue slider. Next, select the blues and turn the lightness all the way down. I also adjusted the blues to include some cyan as well (for maximum effect on the sky.) Even with these extreme adjustments, the H/S/L effect is mild compared to the other methods. Thus, in my opinion, it's not as useful as the other methods. Some may find it more intuitive however.
A common shortcut used in Photoshop to desaturate an image is "cmd+shift+U". This shortcut utilizes the H/S/L layer to create the greyscale image. Thus it's a lightness conversion--not luminosity.
Incidentally, because of the funky formula for L, when I use this layer to adjust saturation of a color image, I always set the blend mode to saturation--again, so it will ONLY adjust saturation and not mess around with luminosity. Similarly for hue adjustments--set the blend mode to hue. Setting blend to "color" is equally good for hue and saturation adjustments.
Gradient Map
Here's and interesting one I don't see get much use. The gradient map adjustment maps the colors in an image to the points along the gradient. Shadows are mapped to colors on the left end of the gradient and highlights are mapped to the colors on the right end of the gradient. If the gradient is a simple linear gradient going from black to white, then the gradient map will map shadows to black, highlights to white, and midtones to the corresponding shades of grey--in other words, it creates a black and white version of your image.
It turns out that the gradient map uses luminosity for mapping. So if you use a simple straight-line black-to-white gradient (ie., starting color of 0,0,0, ending value of 255,255,255, and no in-between points), then you'll get a greyscale conversion that is the luminosity of the image--exactly the same as for the channel mixer using the luminosity forumula. Incidentally, the smoothness setting of the gradient has to be 0 to get the luminosity.
Now you can manipulate your greyscale conversion by adding greypoints to the gradient to specifically control the brightness of midtones. You can also play around with the smoothness setting to modify the appearance of the greyscale conversion.
Simple greyscale conversions are really not the forte of the gradient map--I'm really just mentioning it for completeness. The gradient map is nice when you want to convert an image to something other than just greyscale. For instance, below I used it to convert an image to a duo-tone--red shadows and cyan highlights.
I prefer using a curve for adjustment midtones myself, but perhaps some will find this method more intuitive. Gradient map is usually used for things like duo-tone conversions--it's more intuitive than the channel mixer for that purpose I think.
Of course combining the gradient map strengths with the B&W tool strengths. Here's the more extreme B&W conversion from above combined with the duo-tone effect from the gradient map:
Conclusion
For such artistic endeavors, there is never any absolute conclusion, however here's my biased view of things:
Best overall: Black and White adjustment
Good alternative to try for more extreme effects: Channel Mixer
