Hospital bedding sucks! The blankets don't keep you warm and the pillows are worthless, take at least one of each from home.
Warm stuff for baby is good to pack. A couple of extra baby blankets to pad the car seat.
Reading material. Most hospitals keep women for a couple of days, lots of time in bed, books are great. Nothing too serious or heavy though.
List of Those-who-must-be-told. (numbers for the announcement)
Reference materials. I don't know what kind of birth you're going for, but Dave and I did LOTS of research for the labor and knew we wanted no meds and no interventions, so I had printouts of everything we researched so that Dave wouldn't get flustered the day of and just cave to the Dr's suggestions.
Along those same lines, does your lady have a birth plan written out? that's important to pack. If not, I highly recommend one. Map out plans for all contingencies and discuss and decide how y'all want to handle each one if it comes up. The Drs and nurses dont even need a copy of it, just something to reference in the heat of the moment so decisions are made that no-one regrets.
Have a way to get important paperwork home neatly.
Extra batteries.
Extra clothing for you, birthing can be messy and you're in the splash zone.
Comb and hair ties.
List of names for opposite sex, just in case.
Breastfeeding supplies: nipple balm or lanolin, soothing nipple pads, nursing bra, Mother's Milk tea, nursing pillow, reference book, etc.
I know I don't know you, and you don't now me, but excuse me for a moment because this is really important. Breastfeeding saves lives. You are the most important resource for your lady in the first couple of weeks of breastfeeding. You will need to help her and support her. The first two weeks are terrible! Her nipples will hurt, for me it was worse than the childbirth pain, her hormones will be going crazy and there will be times she'd rather throw the baby across the room than put it to breast. Help her get through those first couple of weeks without resorting to formula. Nothing safer for a baby in any sort of emergency than breastmilk. Hurricane, disease, you name it, baby's best chance of survival is with Mom's milk for most of the first year of life.
Good luck! Congrats!