What is the scruff?
The scruff is the loose area of skin on the upper side of the cat's neck.
Can I pick up a cat by the scruff of the neck?
No, a cat should not be picked up by the scruff of the neck.
It may seem logical, after all, this is how mother cats carry her kittens around (carrying them by the scruff in her mouth). When a mother picks up her kitten by the scruff, he instinctively tucks up his legs and stays still. But bear in mind that young kittens are considerably lighter than adult cats. Carrying a cat by the scruff, with no support places a lot of stress on the neck and spine, causing serious injury, as well as being quite painful to your cat. Also, the mother cat doesn't have the benefit of two hands which are perfectly capable of picking up a cat safely and comfortably, we do.
Male cats also grab the female cat by the scruff of the neck when mating to keep her still.
How should you pick up a cat?
The best and kindest way to pick up your cat is to place one arm underneath the cat, and wrap the other arm around his side, pull him in so that he is close to your body.
What about scruffing to control a cat:
Some veterinarians will scruff your cat in order to hold him down (such as when giving medications or giving him a medical examination). You will notice when he does so, the cat is supported underneath, usually on an examination table, and isn't left dangling.
I am personally not a huge fan of scruffing in any way, but if it is an absolute necessity, then it should be done so with full support underneath the body and only when absolutely necessary.