A great place to start is to ensure your home can addomodate a utility outage for a few days. In the U.S. most common outages last minutes or hours. Sometimes there are events that last for days or months. Start by looking at it per utility Electricity, Heating Fuel, Water, Sewer
Electricity:
On Grid: So you have on grid power. Someone hits a pole periodically. Maybe a transformer blows. Likely most of the time on grid power outages will be limited to a few hours or less. Much of the time, power companies have power loop circuits that can manually or automatically isolate circuits such that the offending segment can be isolated and the power rerouted. Sometimes this can happen within a few minutes. On the other end, do you live in the boonies? is a tree falling on a power line 4 miles away with the nearest line crew coming from 50 miles away in the middle of winter with no roads?
For the brunt of semi urban and urban folks, a good place to start is being ready for a 3 hour outage. Moving up, a person might want to be prepared for a full day outage. Maybe next a 3 day outage, then maybe 2 weeks. Beyond that is real prepper territory. Back to the basics though. What might happen if the power goes out for 3 hours in warm weather. Think through what will happen if this occurs. In 3 hours, likely your freezer won't thaw. Likely anything in the fridge will still be cool or can sustain a slight temperature excursion before power comes back on. Barring any power consuming medical equipment probably a big one will be sump pumps in basements. If the power goes out, your pump goes out. What's a common cause of power outages? storms. Storms bring lighting... and rain.... lightning knocks out power, rain fills sump, bam you've got a flooded basement. Have a sump pump backup. Battery powered? Sure, that'll get you a few hours! Another option may be a water powered sump. These might be expensive to run, but will save you in a pinch. If I Had my druthers, I'd have a 110v primary pump, with a 110v backup pump, then a 12v battery pump behind it, and lastly a water powered pump. All with trigger switches at slightly higher levels such that the primary 110v pump activates regularly. If it cant keep up with the inflow or it doesnt work (power is out or it malfunctions), the second pump can kick on (again if power is still on). This can be a good setup if rain is coming down so hard that your sump can't keep up. If all 110vPower is lost, the 12v pump will kick in. It'll be good for whatever the rated runtime of your pump/battery combo is, maybe from a few hours to a few days depending on frequency of activation, and current draw. So it lasts 12 hours. Your power is out. It's possible you have a local outage, but still have water pressure. The water pressure pump kicks on and lasts until you don't have water pressure any more. if your in an urban area and your water service is fed by a system that has backups and redundancies built in. This could keep your sump running indefinitely. Thats where the four pump system is a pretty sure fire way to ensure you can last through nearly any power outage! As long as we're talking about sump pumps, you need to consider the discharge especially in climates that freeze. A common problem in those climates is sump discharge locations freezing shut, not allowing the sump to discharge. There are a few common solutions for this. Probably the first place to start with this one is looking at how the discharge piping is laid out. It should be pitched toward the discharge so no standing water is left in the horizontal pipe. If the pipe goes outside the home and connects to another pipe it should have an air gap or all be freeze proof via heat tracing. An air gap will allow the lower pipe to freeze if it gets blocked, then water can still flow through the gap and discharge outside the home. All sumps in northern climates should have this. One other means of reducing the risk is to install another pump and discharge. A bit more effort and cost, but even more likely to not have sump problems with this in place.
Internet: How dependant are you on your home internet? Have a backup? A backup for a backup?
Things to consider:
As a backup, you might keep an old Iphone that supports tethering and keep a prepaid sim card with some available data on it. Might cost you $20 for the sim with some data. These usually have an expiration or a monthly minimum fee. Either way, it could save you if you have no home internet and you lose your cell phone.
Satellite backup: How bad do you want backup? a satellite backup would give you piece of mind but they are susceptible to poor weather conditions.
How about voip? Want a home phone but don't want a dedicated line? try some sort of voip service. Run a voice line over your internet connection!
Wireless Internet: something like http://myairfiber.com/ Might give you a backup service that doesn't rely on wires thats more dedicated than a cell service.
Off Grid
Gas:
Water:
Sewer: