You should check with the hospital to see what they require, but if you're in the U.S., honestly, the less you bring, the better.

1) For the baby, you need only a going home outfit, and a car seat (in your car). You might want to pack two sizes (newborn and 0-3 months), as you never know which one will fit your baby. The hospital will have everything else -- diapers, onesies, hats, blankets for the stay there. You don't want to bring your own stuff, because it can get mixed in with the hospital's stuff and will be gone. Make sure you take home all the stuff that's they have there for the baby -- extra diapers, blankets, wipes, etc.

2) For you, also not that much, as you won't use most of the stuff. Some key items that you may want include:

-- cell phone charger
-- pen and notepad
-- shower shoes (flip flops) and some other kind of easy to get into slipper, like a scuff (you're not going to want to be bending over to put something on your feet)
-- a beach towel or other towel, as if you think you'll be there long enough to take a shower, their towels are small and horrible.
-- if you have long hair, a hair scrunchie
-- chapstick and hand cream (hospitals are very dry)
-- small tube of Lansinoh ointment (although the hospital will probably have samples for you to use when you're there) Your nipples will likely be a mess as you try to breastfeed.
-- a small toiletries bag, although my hospital had the sample size kit for everyone, which I wound up using
-- A hoodie or other jacket/robe to keep over your shoulders, especially when trying to breastfeed.
-- For your going home outfit -- loose pants (sweats, yoga etc), and loose top
-- some big old underpants. However, I really liked the disposable mesh ones they give you in the hospital for when you are there
-- one pack of very large sanitary napkins, although the hospital will have those as well.
-- a few snacks (power bars, etc), in case your hospital has weird food hours and you wind up wanting to eat when it's all over and it's not "Meal time."I had a planned c-section late in the day, and so I hadn't been allowed to eat that day, and they wouldn't actually bring me food until the next day lunchtime. I was starving, so I ate some food I had snuck in.

Because I had a planned c-section due to prior uterine surgery, I didn't really have a big plan. Had I gone into labor on my own, I would have had had to go over there fairly quickly. But in general, do plan to labor at home as much as possible. And keep in mind that no matter what you think you may want to do, the plan on the day may change. Don't get too wedded to any one idea of "how I'm going to have my baby". It's good to be knowledgeable and have some wishes, but things almost never go exactly as you pictured them. Don't let it disappoint you -- the key is to go home with a healthy baby and mom.

Good luck!