This is a sample list of things you might take on a week-long trip hiking in a wilderness area. Even more than with other kinds of travel, packing for this kind of trip requires compromises between keeping weight down and making sure you bring everything you'll need, because you have to carry it all with you. Depending on where you're going and the time of year, some of the items may not be useful to you, and there are inevitably additional items you'll want to bring along, but this should give you a general idea of what you'll want to pack. For information and advice about gear selection, see Wilderness backpacking and Cold weather.
For some of the equipment it is enough if one or two persons in the party have them. This is true even for some of the clothes: some spares are needed mostly when something breaks or gets drenched, which may be unlikely to happen for all the party.