There is nothing worse than going into the backcountry underprepared. Here is a list of basics that we require for a Wild and Weightless backpacking trip. If you're interested in learning more about backpacking gear check out this article from REI. If you would like to pack additional supplies to stay comfortable that is totally up to you!
Sleeping bag (rated to at least 20 degrees)
Headlamp (with extra batteries)
Backpacking stove, fuel, pot see example here
Two large Nalgenes
Snacks for 3 days
Sunscreen 50 SPF
Personal Med Kit