Babies need to learn to self-soothe, and letting them cry themselves to sleep is the simplest way to do this. Essentially sleep training, the Ferber Method is perhaps the most well-known and controversial program that urges parents to limit physical contact with a crying child at bedtime and throughout the night. If followed properly, it does not promote abuse or negligence in any way. It teaches a child that crying will get nothing more than a brief check-in from Mom and Dad, and it also allows everyone in the home a better night's rest.
A mother should be aware of when her baby is crying and if he/she/it needs attention(diaper changing, a bottle, a nap, or another necessity) then it should be given to the baby. However, sometimes, babies cry for no reason, other than to cry. If a mother tends to the baby every time it cries, it will think every time that it cries Mommy will come running to help. This can lead to other attention issues as the infant gets older and matures.
Babies cry, babies cry for no reason sometimes. If you attend to a baby every single time they cry they will cry for no reason other than "where is mommy?" and that will get annoying and frustrating for the parent and anyone who ever babysits the child. As long as the baby isn't needing a change of diapers, food, sleep, or anything else that is a necessity, let the kid cry it out. Coddling and doting the baby won't do anything but make it cry nonstop, good luck finding a babysitter that sticks with you with that sobbing baby! YIKES!
Allowing a baby to "cry it out" is one thing but one should consider the length of time allowed for the behavior. There are other methods one could use rather than simply allowing the baby to "cry it out". One should attend to the child and try to understand the reason for the frustration and work on the situation. I can't see how allowing a child to "cry it out" could be beneficial to the child nor the adult.