Besides the obvious:
A good support system. Being a new mom can seem daunting, having a good support system can really help with that and is necessary for your sanity.
Other than that:
Two diaper bags (one for you and one for when they are with someone else)
Lots of spit up blankets
A Swaddle Me----Best thing EVER!! Trust me, it works wonders.
Car seat and stroller obviously
Lots of bottles (whether you're breast feeding or not)
A swing that rocks and/or vibrates
A bassinet at first--We didn't move ours to her crib until she was 8 months
Those things all helped us a great deal for the first six months, and some still do. :)