Several years ago I put together a unit for camping and hunting trips. 12V 120AH SLA deep cycle battery, 1000W power inverter (12VDC to 120VAC), 40W PV solar panel with 12V charge controller, all mounted on a wheeled dolly.
Runs CFL and LED lights all night. Keeps cell phones charged. Powers the laptop computer. Will run a radio, small TV, small refrigerator, even the Mr. Coffee in the morning. Then 6 to 8 hours in the sunlight and the battery is topped off for the next night. Total cost was about $300.
Between trips I keep it set up at home as a back-up for power outages. Solar panel has 50 feet of line so it can be set up remotely outside. Will run a couple of lights almost indefinitely. Will power the blower on the forced air gas furnace. Will run the refrigerator for 10 minutes every hour to prevent frozen food from thawing. Will run a TV, power tools, etc, but those can drain power very quickly, and with only 120AH storage you can't be a power hog.
Shortly after putting this together the power went down at my club while the Super Bowl game was on. I ran home, picked up my unit, put the game back on for a couple of hours. Needless to say, I didn't have to pay for my beers that day!
Last year I bought a 21' travel trailer. It has 2 on-board 12V deep cycle batteries, charging from the tow vehicle while driving. I will be adding hook-ups for my other battery (bringing total storage to over 300AH) and a couple of PV solar panels (will probably go for about 200W capacity for this use). Keep the camper parked by the house so an extension cord can bring the power inside if needed. Thinking about a small gasoline generator (3-4 KW) with 12VDC charging capability, should be able to fully charge the batteries in under an hour if needed with minimal gasoline consumption. For now I'll just start the truck and let it idle for a half-hour if I see my batteries are getting low at night.
A full off-grid or grid-tie system for the house would be very expensive and take a long period to pay for itself. A small system for back-up, camping, etc, is easy and relatively inexpensive.