Since baby number three arrived last month, I've been thinking about all the baby things that I absolutely wouldn't live without (as well as those that I never opened). At the top of the list is definitely some waterproof pads. I use them for everything (changing pads, to put down on the changing table to stop pee from "traveling,"). I love using them in the crib for when my baby leaks through her diaper. It sure beats having to change the whole sheet in the middle of the night...
Cloth diapers. I love them. I love that I'm not throwing my money away every 3-4 weeks on a new box of diapers and the amount of trash my family of 5 puts out to the curb every week amounts to about 1 trash bag full (yes, its true). I've got both a set of prefolds with a snappi and they work great for the early days and they are economical. I also have some Bumgenius 4.0's that are awesome and do double duty in our house since my 2.5 year old wears them too. Adjustable, one-sizes are a great way to save some money. I also like to support local businesses so check out Diaper Junction in Virginia Beach, Va. They have some great sales on diapers throughout the year so you can save even more money.
A fan or a sound machine are also on my list of must haves. Anything to create a bit of noise so baby is not falling asleep in pure silence. I use a fan to create white noise in boys' room so they don't hear us bustling around downstairs and wake up. I've got a baby sound machine that also has a projector on it that plays white noise (heartbeat, ocean waves, rain) as well as songs that I put on when I put my 6 week old down for the night. It's like a mobile but doesn't hook onto the bed and just sits on the floor. It also doesn't require batteries which is a good thing in my book as they are expensive and not very environmentally friendly.
A good baby carrier is a must. I have an Ergobaby carrier that I wouldn't live without (especially since I have two older children under the age of 5 to chase around). It's comfortable to wear and my baby loves to be in it. It can be worn on the front or after about 6 months of age can also be worn on the back.
Those are my must-haves. I know there are definitely other things that you need for a baby, but these are the things that I think are often forgotten or overlooked. :)