I have a small copper water line that supplies a hose faucet out on the front of the garage at my house. One year I forgot to turn off the water to that line from inside the house and the pipe froze. Luckily I had nothing in the garage that could be damaged by water, but even still...it was not a fun experience. It made a loud kaboom and next thing I knew there was water and ice everywhere in the garage. Then I had to go shut off the line, cut out the pipe, and repair it (which was not fun out in the cold and icy garage).

Anyway, we do have a generator wired into the house. A few of us in the family had them installed back in 1998-99, because of the whole y2k thing. We decided on a diesel unit, as I have a few 1000 gallon tanks of diesel on hand (since I'm in the construction industry). This is what we had it set up to run:

-basement sump pump
-a few hall lights, the kitchen lights, and the ceiling fans in the bedrooms
-a few key 110v outlets: in case I need to power some small appliance
-first and second floor furnace
-our three refrigerators
-the two electric garage door openers
-the water heater
-the washer and dryer
-the kitchen microwave
-the central alarm system* (security/fire/carbon monoxide) *This has a battery backup, but I made sure it would get power anyway.

Off the top of my head, these are things I decided not to wire in after careful consideration:

-Central air> This draws an absurd amount of power and I didn't really feel it necessary with the ceiling fans in the bedrooms.
-Stove> The range top is natural gas, so that can still be used to cook.
-Security Cameras> This has its own backup power supply.
-Modem and Router> This is backed up by its own UPS.
-Main desktop Computer> I didn't want to hook this computer into the dirty generator power, but it does have a UPS that will keep it running for at least 15 minutes in a power failure. Otherwise, I've got a few battery-powered laptops.
-Main cable tv box and main tv> I've got a portable tv and a few portable am/fm radios for information, so I didn't bother.
-Phones> I've still got a self-powered landline, so that doesn't require generator power as long as you have a wired phone plugged in (of which I have two in the house, kitchen and master bedroom).

For me, the most important things to have powered were the sump pump, the furnaces, the refrigerators, the garage doors, and the alarm system. As they tend to cause me to worry if they aren't working. Also important to me was the hot water heater, just because it's so annoying when that goes out.