Clothing

8 undershirts or onesies (mix of short-sleeve and long-sleeve) [thanks Janet, Peter/Anna]
5 nightgowns (for use until the cord falls off)
8 one-piece stretchy sleepers (go for ones with zippers; new moms swear by them!)
5 pairs of pants
2 newborn hats
8 pairs of socks or booties, to wear with nightgowns and outfits
2 pairs of scratch mittens, to keep baby from scratching his face
2 cardigans or jackets, more in winter
heavier 1-piece sleeper
Laundry detergent for infants

Blankets

Feeding

Lots of bibs
Burp cloths
Breast pump
Milk storage containers
Nursing pillow
Nursing bras (if buying before baby is born, buy one cup size larger than your pregnant bra size)
Breast pads (disposable or washable)
Lotion for sore nipples

2 four-ounce bottles with nipples
2 eight-ounce bottles with nipples
Bottle and nipple brush
Formula (be sure to check expiry date and note the lot number in case of recalls)
Thermal bottle carrier

If you are using disposable diapers:

Two boxes of newborn-size diapers (it's better not to buy too many in advance in case your baby is large or grows quickly)
1 diaper pail
Changing pad
Baby ointment or barrier cream to prevent rash
Disposable wipes or a couple dozen washcloths for cleaning baby's bottom

1 plastic infant tub (or use a large dishpan in the sink, or take baby in the bath with you)
12 washcloths, not used on baby's bottom
Baby soap or cleanser
Baby soft-bristled hair brush
3 soft-hooded towels