We do it at all different ages. As Aart said a big part of that is how you want to cook them. The older they get the more flavor and texture the meat has so you need to cook then according to their age. There are all kinds of different ways to cook them at any age but (other than pressure cooking) the older the chicken the less heat and more moisture your method needs to use. You did not say cockerels, you said chickens, so you could be talking about pullets too. As far as cooking methods, cockerels and pullets age differently. If you have a certain cooking method in mind we may be able to offer some suggestions.
Some people butcher cockerels as young as 12 weeks. There is very little meat on them but they don't want the cockerels to hit puberty and start to crow or start chasing the females. Those can be fried or grilled. I like to wait until about 23 weeks for cockerels and probably close to 8 months for pullets so I can see what kind of eggs they are laying to decide keepers and those for meat. I bake those cut into pieces and coated with herbs for about 3 or 4 hours at 250 degrees F.
Another issue is that we all have our own tastes and expectations. Our chickens. cockerels and pullets, are going to be older than he Cornish X you are probably used to from the store so they will have more texture and flavor. Some people find that grilling chicken (especially cockerels) after 12 weeks leaves the meat too tough to enjoy. Aart's age is 16 weeks. Another member has a cut-off of 14 weeks for grilling cockerels. We all have our favorite method of cooking and ages, sometimes it takes a bit of trial and error to find what suits you best.
Good luck!