I encourage parents of young babies to pick up their baby when he is crying and see if they can help him fall asleep. Many young infants don't know how to settle themselves and need some help with quieting down in order to fall asleep. Techniques such as rocking, patting, and snuggling can help lull a baby to sleep.
You can't spoil a baby this age by picking him up; infants do need comforting and should have their needs met. Thus I don't generally recommend just letting a one-week-old infant cry himself to sleep. If parents have been trying to quiet the baby for a while, and he's still screaming despite your best efforts, then, as a last resort, it's okay to put the baby in the crib and let him "cry it out."
This does not mean that you should spend a child's entire infancy coaxing him to fall asleep. Every child to learn how to fall asleep on his own, but many children need help with this in the first few months of life. By three months of age most infants have settled down and no longer have long periods of crying.