Much of the Northeast blacked out for a while in 1977:
New York City blackout of 1977 - Wikipedia, the free encyclopedia
And again in 2003:
Northeast Blackout of 2003 - Wikipedia, the free encyclopedia
We lost power for a week in an ice storm in '01. Texarkana lost it for over 10 days.
Your house goes dark, of course. If you have a land line, it usually stays on; the telcos have their own backup power. Hospitals and nursing homes usually have generators. Police stations generally don't. After the tornados of '07 Mountain Home, Arkansas was dark except for Wal-Mart.
Locally, the refrigerator-sized traffic light control boxes don't appear to have any batteries in them; when the power goes off, we lose traffic signals. You can't buy gas anywhere; every gas station has electric pumps. You can't buy gas most places if the phones go down, since everyone is connected to the mothership somewhere else. Cell towers usually have generators, but in some urban areas they might not, due to the crazoids who hate the antennas and manage to get installations restricted in various ways.
After a week or so you'll lose water. The water towers hold 3 to 10 days worth, most places... but without the pumps to refill them, when it's gone, it's gone.
Some places, the sewer system depends on electric pumps to stairstep the flow up changes in grade. If your house is downhill from the local sewer main, you probably have a pump in the house or out in the yard. And around here, if you have a fairly recent septic system, code requires a macerator pump before the settling tank.
Most newer gas water heaters use electric ignition instead of a pilot light. They're not designed to be lit with a match, either.
I've seen new gas meters with digital displays on them. I don't know anything about them (or where they get their power from!), but you might be concerned about interruption in your gas supply if the power goes out in the winter.
Basically, if your power goes out, fill whatever you have with drinking water if you don't have any stocked up already. And be aware the toilet may quit working after a while. Other than that, you're on your own...