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. :)

Moms Expertise
    8Theresa Gould
    Good advice.f
    About Theresa
    Current: Butte, Montana
    Birth: May 18
    On since: Feb 24, 2014
    I am a new mom w/ a wonderful baby girl & her amazing Daddy who I'm so lucky to call mine. I work hard at my FT job w/ our local Big Brothers Big Sisters. I try everyday to be the best mom & girlfriend I can be. I am so proud of myself & my family!