Start with the bones of the house...
Take the pipes and wires out of the walls, the sheet metal from the air ducts, some of the wall studs and solid wood doors. If the house has a metal roof, take it as long flat sheets of metal can be very useful for rainwater harvesting. Same for closet shelving, gutters and window panes.
Next, look at the appliances...
More sheet metal from the covers, motors and heating elements from inside. The water heater is worth taking intact as it can server as a water container. Magnets from the microwaves. There is probably a barbecue grill and maybe a generator in the garage. Don't overlook the ceiling fans, lamps (with light bulbs) and extension cords.
Soap is always welcome, but bleach and ammonia are potential weapons. Bug spray can be used like mace. Raid the liquor cabinet, medicine cabinet and any cigarette stashes for trading supplies. Check the garage and shed for fertilizer and if there is a pool, find the chlorine tablets.
This is America after all! Butcher knives, lighters, carpentry and gardening tools can also make effective weapons. Don't rule out the possibility of finding decorative swords, bows and crossbows. Keep your eyes out for ammo, bolts and arrows. Look in the cars for snow chains, tow chains and gasoline.
Warm Clothing, blankets, towels and sheets (for bandages), first aid supplies, paper, pens, scissors, cutlery, cooking pans, toilet paper, toothbrushes, deodorant, mirrors (for signalling), batteries, vitamins.
Obscure but Possible
Check the back yard for fruit trees and berry bushes. mason jars and canning supplies, free weights and portable exercise equipment, scuba equipment, camping supplies.