Well, OK, it's confession time. You (and your baby) can live without many of the items below. But even apart from the natural desire of parents to make their baby's life as easy as possible, many of these help ensure their health and safety.
You'll need an infant car seat, even if you don't intend the baby to go out often. Many hospitals will require you to have one before they'll release mother and child. If you don't have one, some will supply you with a temporary. They have their insurance regulations to follow, you know!
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You'll want to carry your baby around, but your arms will get tired. A good strap-on baby carryall will do wonders for you and your child. Like a good backpack (whether worn on the back or front), it will free your arms and save your back. They're also great for encouraging the bonding between parent and child that comes from physical closeness.
An adjunction to that is a good stroller. Even with a good carryall, babies can get heavy after a while. A sturdy stroller with a braking mechanism for hills and near the curb is always useful. Having one with an adjustable hood allows for the right amount of shading and sunlight filtering, too.
Both at home and away, a good diaper changing station is never wasted. A portable one will help you during those spontaneous moments that always seem to come at the most inconvenient time.
There are times when you want to rest your baby to relieve your arms and still want the baby to get a great view. A bassinet or cradle with adjustable arms is the perfect solution. Naturally, you'll want one that is ultra-sturdy. Make sure there are no sharp corners and look for ones that provide a means of securing blankets, buttoning in cushions and other handy add-ons.
As your baby develops, providing him or her with a means to exercise those burgeoning muscles promotes health and psychological well-being. A rocking chair with straps is useful. A bouncy seat with musical danglers is another good option. Make sure that any noisemakers are removable. You don't want to drive yourself crazy!
Speaking of music, a good CD or iPod-type player with speakers can be a great addition to the 'baby toolkit'. White noise helps some young ones deal with colic. Classical music helps young minds develop. Gentle sea sounds and lilting tunes provide a peaceful atmosphere that will help both child and parent.
Of course, there are a whole range of toys that serve a number of good purposes. Babies are exploratory by nature. Providing safe things that will go into the mouth, but only so far, is one category. Building blocks of various sizes help the developing mind learn about shape, volume and other basics. Sound-making toys help them correlate self-initiated movement with the resulting noise. Learning cause and effect early is a big boon.
Don't forget to stock the medicine cabinet with that whole range of needed items for emergencies!