A UPS system might keep things running for a short time, but being able to monitor when the power goes off is invaluable, especially when using off-grid technology.
I was having problems at my place with the power going off, and shutting down the fridge and freezer, so I set up this project to notify me when it was happening.
Fortunately the router is on a UPS, so it wasn't too hard to get a message out, even if the power was off. I've got an Arduino Leonardo attached to a WiFi shield and a custom UPS shield. I guess I could have run the Arduino from the UPS as well, but I still needed to sense if the power was on or off, and when I thought about a UPS shield for the Arduino, it was easy to add power sensing. In addition, the analogue pins on the Leonardo make it easy to monitor the battery voltage, so that I can use it as a power supply for the setup to run untethered (away from power), and report battery voltage.