Some great ideas were mentioned above (especially the focus points and paperwork ones!)
Some things that really helped me:
My own toiletries — nothing felt more refreshing than waking up the morning after delivery and taking a shower using my own toiletries. I brought the basics: toothbrush, toothpaste, shampoo/conditioner, body wash, deodorant, and lotion in travel sizes.
Pads and undies — I know the hospital supplies pads but I brought a big bag of my own, as well. They were a saving grace when I ran out of my hospital stash. Sometimes it takes a while to receive items you ask for and not having to wait for a pad was lovely. I also packed plenty of undies. I went through quite a few pair but I brought them home, washed them and continued to wear them until I was done passing lochia. Then, I tossed ’em. 🙂 The hospital does have the mesh undies that you use once and toss but I didn’t care for their coverage, or lack thereof.
A Boppy pillow, or something similar — my Boppy was a workhorse through the first 6 months of breastfeeding! It’s also useful for bottle feeding. I swear, it saved me from many kinks in my neck and shoulders. If you plan to BF, you may very well find yourself in some funky positions at first while you and DD try to get acquainted with feeding. It’s not safe for her to sleep in alone but for feeding, it’s lovely.
Snacks and drinks — while you may not be able to eat during labor and delivery, I did have some gum on hand to chew through the pain. I also had some light snacks and water bottles on hand for the nights we spent in the hospital. I work at the hospital I birthed at and I know “food food” (items other than crackers and ice cream) isn’t available after a certain time. If you don’t get hungry, your SO might.
For baby — the hospital will supply diapers, and plenty of them, so don’t feel like you have to pack hoards of them. I brought a few different PJ sets in varying sizes and a going home outfit for Madi. Bring some long sleeved outfits and plenty of little socks as it gets cold quickly! Also, one thing you may not think of but should pack is a pair of tiny nail clippers. Madi was born with long nails and when she slept, I trimmed them to prevent her from scratching her face. I also brought my lanolin cream for BFing. It helped relieve my chapped nipples. I didn’t need my nursing pads because my milk didn’t come in until the day after we went home.
And…last but not least, bring your camera! My favorite photos (ever) are of Madi’s first few days. I didn’t bring a laptop (didn’t have one at the time) but personally, even if I had, I wouldn’t have found time to use it. Try to minimize what you bring because the hospital gives you TONS of stuff, too. You don’t want to have to unpack and sort too much when you get home.
I know that was a bit jumbled together but hope it helps.