1. DESATURATE
2. GREYSCALE
3. GRADIENT MAP
4. LAB COLOR ( USING THE LIGHTNESS CHANNEL )
5. CHANNEL MIXER (DEFAULT SETTINGS)
6. CHANNEL MIXER (USER DEFINED SETTINGS)

This is the result of converting by DESATURATING the Colour Image by using Image/Adjustments/Desaturate.
The result is very dull, most of the colours fall into the Midtone band and there is not much room for manipulation.

Verdict: Easy to achieve but results poor

This is the result of converting the colour image to GREYSCALE by selecting Image/Mode/Greyscale.
The results are much better than Desaturation, but little room for improvement.

Verdict: A good method for the Beginner, but as the beginner becomes more competent there are more complex methods that give better results.

This is the result of converting by using a Gradient Map Adjustment Layer
Layer/New Adjustment Layer/Gradient Map, then choosing the Black, White gradient. This method gives better results than the Greyscale method and because it maintains the colour information the tones can be modified by applying other layers such as Hue and Saturation.
Verdict: Better option than the Greyscale or Desaturate method.

This is the result of converting the Image to LAB COLOR, selecting the Lightness channel only and converting the image back to greyscale.

Verdict: This method gives a fair tonal conversion, but because some of the colour information has been discarded it lacks the versatility of the Channel Mixing methods.

This is the result of converting by using a Channel Mixer adjustment layer.
Layer/New Adjustment Layer/Channel Mixer then tick the Monochrome box and adjust the sliders to 68 Red 24 Green and 8 Blue.
These settings give a good overall balance to most images but should only be regarded as a good starting point to fine tuning by mixing the channels to suit the image. This methods keeps the colour information intact, which enables further manipulation of the tones using Hue & Saturation Adjustment Layers.
(see my Photoshop Tutorial 9)
Verdict: This is a method for the more advanced worker but coupled with the use of other adjustment layers such as Hue & Saturation, Colour Range and Colour Balance it gives very good results.
This is my preferred method.

I hope that the above comparisons have helped you to chose a method that suits you.
The better methods are too complex to embrace in this article and in the future I will produce more in depth tutorials.