The natural way to feed a newborn baby. Unless otherwise contraindicated, this is the best way to feed a baby for the first few months of its life.
Not only is breast milk nutritionally better (and cheaper) for the baby than any other baby food in the market but it also helps create a strong mother-child bond. There is also evidence to show that breastfed babies are less prone to gastroenteritis than bottle fed babies. This may be due to antibodies passing from the mother to the baby through the breast milk. The World Health Organization (WHO) has recommended that all babies be breastfed for the first 3 months of life. A recent study has suggested that breastfeeding for more than 4 months does not confer any additional advantage to the baby, so it might be a good idea to think about weaning then.
On the flip side, drugs have been known to pass through to babies through breast milk - therefore a mother addicted to heroin or alcohol (or any other drug of abuse) should not be breastfeeding her infant (and indeed should be a target of social services). Some viruses including HIV (causing AIDS) can also be passed on through breast milk so this is another known contraindication to breastfeeding.
A less known fact about breastfeeding is that it is a pretty good form of contraception. Breastfeeding on demand (the baby's demand, that is) alone is a proven contraceptive with a less than 10% failure rate for the first few months. This works because the prolactin levels that are induced by demand breastfeeding inhibit the normal ovulatory cycle. This should not be relied on as a sole form of contraception however, as most women in western society do not breastfeed their babies as often as they should and because they may well be fertile before their first period following childbirth.
Western society seems to drift between approving and disapproving of breastfeeding in public. What is there to be ashamed about this when there are places such as topless beaches?
Update - March 19th, 2001 - just for the record, between radlab0 and momomom's writeups below, I tend to agree with momomom.
And yes, IainB is correct, breastfeeding does reduce a woman's chance of getting breast cancer. Women who have an infant at a younger age and who breastfeed their infant have a lower risk of getting breast cancer. It has something to do with the fact that making use of the mammary glands for their actual intended purpose, lactation, is somehow better (in terms of cancer risk) than just letting them go through the 4 weekly menstrual cycle period of hormone cycling.