2 or 3 packages of newborn diapers
Wipes
Changing stations on each level where the baby will be.
Ask your Pediatrician what kind of Diaper Rash Cream they recommend... Have more than one tube
Wipe warmer
Bouncy seat
Swing
Bunch of those head support rolls- you can put them in the swing, the bouncy seat, the car seat
A lot of the nasal aspirator they use in the hospital
Front carrier or sling
Clothes, we used onesies and jammies almost exclusively the first month or so...occasional outfit when someone would come over or whatever, but mostly easy on, easy off stuff
Sleepers - The Carters kind that are made from Terry Cloth with feet
Onesies or snap t-shirts
Little infant hats - especially if you live in a colder climate
Socks!! We used them on their hands as well, since most of their outfits didn't have the handy hand covers like the hospital shirts.
Receiving blankets for swaddling, as they need to be kept warm at first while their little bodies get used to the outside world.
BURP CLOTHS...babies spit up more than anyone would ever dream is humanly possible...for a long time. We bought the cloth diapers and used those...worked great.
A rectal thermometer and Vaseline (This is Vital! You do not want to be without one at 4am if you need it).
Pacifier - even if you are planning to nurse- have one (or 4) in the house, boiled, just in case you need it to get through that first week of Breast Feeding Baby Nail Clippers
Stuff for you:
Healthy meals & Snacks, Easy access to Water (and ice), pads - your favorite kind - Lots of them, the overnites are good for the first few days home, nursing bras, nursing pads (what are those things called that you put in your bra to soak up the milk?), I was VERY COLD the first few days home - something to do with my hormones, I'm sure. We cranked the heat in the house up to 74, and I still wore flannel pajamas for the first few days... Help - Mom or Mother in Law (even if you can't stand them) - someone to let the dog in and out, hold a fussy baby so you can rest or shower, possibly (if you are lucky) they will cook something - or pick up lunch? Husband's can be good for this too - but sometimes a third pair of hands is really nice (and they come with experience!).
Squirt bottle for use in the bathroom. You'll probably get one in the hospital
For the House:
Food
Beverages (both alcoholic and non-alcoholic)
Paper Products (Paper Plates, Cups, Silverware, etc)