We live in an area of frequent and often long power outages, and used portable generators for several years, then installed an automatic standby generator. Here are our critical reasons/circuits:

Critical:
1. Sump pump. This automatic pump keeps the basement dry by allowing water to flow into the sump, essentially a 55 gallon drum buried below the basement floor. Without it, the basement will fill with water, destroying everything it touches, e.g. the HVAC system, hot water heater etc etc etc. Not a theoretical threat in our area. The first year we moved in, a storm took out power and a neighbor who did not have a generator ended up with 3 feet of water in her basement. And such a "flood" is usually not covered by your homeowners insurance. To us, this was and IMO is a fully sufficient reason by itself to have a generator.

Other significant reasons:

2. Fridge: food and insulin. Insulin is expensive to replace, especially when I try to keep a minimum 3 month supply on hand.
3. Medical devices: power assist devices for DW so she can move around the house. The techs who installed our automatic standby generator told me that 80% of their installations were due to medical devices needing power.
4. heat and hot water: both gas operated, electricity only to power controls and fan.

Convienence:

5. TV and internet.
6. a few lights here and there