I think a "must have" list really depends on the parents and their lifestyle. What I consider my "Would like to haves" for the baby Im expecting up to around 1 year old (I would say I already have about 90% of this stuff but I have to see if its still serviceable):
Diapers- we wash every 2 days and my babies tend to go through a LOT of diapers. Both girls went through about 1 an hour for the first 3 weeks.
30 AI2s (the only diapers my hubby will use)
15 fitteds/ 3 covers (I prefer these and will use them when hes at work)
diaper pail/wet bag (I have a very powerful sense of smell so keeping the diapers where I can't smell them is hard)
50 or so cloth wipes (just so you know, they come in very handy as nose wipers, hand wipers, feet wipers, picking up spills, oops I forgot my nursing pads etc. Even as a burp rag)
Feeding
My Breast Friend Nursing Pillow (I have a bad back from a messed up epidural from my first, because of that first couple of weeks can be very painful, this nursing pillow really helped me keep with it during the worst part with my first)
20 sets of reusable breast pads (I know I leak a lot. Of course most first time moms won't know so they can get less and buy more when needed) OR disposable pads OR a combo of both.
Tubing/new shields for my breast pump. (I have an oversupply so even though I don't use a babysitter and don't work I need it to help get the baby latched on properly for the first few weeks)
10-15 burp rags, my kids are spitters so if I don't have these Im changing my clothes every time I feed them.
Gear:
A bouncy seat- to put the baby when Im using the bathroom, showering or taking a bath. Also useful for when Im giving the girls a bath.
A pack and play- quick safe spot to put them when I have to do something like taking a hot pan out of the oven. Please don't wear your baby and work around a hot stove/oven, my husband did that and my youngest ended up with a terrible scar because of it.
A swing (this is a maybe)- I do a lot of hands on stuff with my daughters and we are doing home school preschool things right now so at needs I need both hands. However, Im waiting until the baby comes to see if they even like it before I buy it. This is for up to about 4 months.
An exerciser- for after 4 months. Both my girls loved theirs, it was the only way I got anything done around the house. They spent two 20-30 minute sessions in them a day and I got to have a clean house and home made meals because of it.
Car seat- Im getting a bucket. One, its easier for me to get them in a bucket and into the car, two most convertibles Ive researched don't necessarily fit a newborn well. I want to make sure they have a seat that fits well and is easy to use.
Carriers: I love carriers and find that one doesn't necessarily work for everything that we do.
A wrap- I use this for when Im taking the girls to the park, I find it the easiest to use when Im lifting and helping older kids on and off the jungle gym. Also we go to the beach a lot so Im making a gauze one for use on the beach.
A ergo- for an older baby for with insert for DH to use with the newborn. Its the only carrier he is comfortable with.
A mei Tai- for when we are hiking and Im carrying the baby. Im not the biggest fan of the ergo, its straps are to wide for my shoulders and tend to fall off.
Bathing:
some kind of gentle soap. I don't use it often but with DD2 DD1 decided to give her a high five with mud and get mud all over her. She was around 4 months old at the time and I hadn't used soap since coming home from the hospital and I used it to get all the tape from the IVs off of her.
Small towels- I know most people think its optional but with my girls having the baby wrapped in a big towel would be a disaster waiting to happen.
Health:
thermometer
bulb sucker(the hospital didn't provide anything for us to take home so Im glad I had a few, I had to order them online as well since the local PX didn't have one and I couldn't figure out the Japanese ones out in town)
Sleeping:
A couple larger blankets for swaddling. Id start with 2-3 and if they like it get more. My first loved being swaddled, my second wouldn't sleep if her arms were in a blanket.
A co-sleeper- didn't need it for my first two but this time we will have a 2 year old sleeping with us most of the time and a 4 year old sneaking in when she needs some TLC so having a designated hands off baby space is important to me..
Some kind of soft night light. My girls were experts at pooping in the middle of the night and it would have been great if I didn't have to turn on the main light to change them.
Clothing- My kids are always dressed in more than just a diaper. I don't know why but Ive never been able to bring myself to leave them in a diaper or a diaper and onesie all day. Im odd.
Winter (Im due in Feb but over here it never really gets cold)
1 jacket (don't need for us since the coldest it gets is like 60)
2 sweaters
14 long sleeve onesies (my kids are spitter upers so they get changed at least once a day)
7 pairs pants
7 PJs
7 recieving blankets ( I wrap them up in a blanket whenever we go out if they aren't in a carrier. I find it helps keep hands away from them)
1 nice Sunday outfit
1 special coming home outfit.
Summer: same only short sleeve and only 1 sweater.
Now what do I absolutely have to have:
Car seat
Boobs
Bed
arms
a couple outfits
and at least 7 diapers so I have time to do diaper laundry before needing the diapers again.