Individual device/appliance backup power unit with Rechargeable battery (BUPURB).
Utilizing a small product package, I see the need for a small (i.e., USB cube, smartphone, or multi plug strip size) and inexpensive ($10) rather than a large centralized generator or large battery unit for powering everything costing $1000's. Plug and play type unit which does not require re-wiring or expensive adaptors.
An individual backup power unit with a rechargeable battery (BUPURB) for lamps, lights, communications, etc... should be inexpensive. Each BUPUB unit would be able to be plugged into an electrical outlet for use and/or recharging and further connection to the device.
When the electricity goes off, the battery automatically kicks on to power the device (i.e., lamp, wifi, TV, water pump, etc...). Each device would have its own backup battery. Surge protection could be included.
The maximum run time should be a few hours as most power outages I've experienced are of short duration. The BUPURB could be offered in different capacities to run different types of appliances or devices. For instance, 50 W of backup power for a lamp. 100 W for cellular phones, etc...
Moving forward, it should be possible to offer a fuel cell alternative or solar recharging accordingly.