You likely have all sorts of things in your home right now that would serve you well in an emergency, with a few additions and some organization, you'll have a functional kit and contingency plan.
Creating a home emergency kit can be a simple to enormous undertaking depending on the level of energy and preparation you want to invest into it. Most people are on the "Stay warm and fed until the power comes back on" camp, not the "Prepared for zombie apocalypse" camp, and though it never hurts to prepare for the worst we'll be focusing more on the former than the latter.
Once you read over the following tips you can adopt them to fit your needs based on your locale and weather, size of your homef, and how much storage space you have available.
Know The Lay of the Land: Before all else you want to know how to control your home in the event of an emergency. Do you know where the water shutoff valve is? The emergency shut off valve for the gas? Which circuit breakers go to which part of your home? Many home emergencies can be quickly neutralized by knowing how to shut down the infrastructure of the home. Make sure the rest of the people in the house know how to do things like kill the water or electricity. It may not seem critical now, but if a pine tree comes crashing through your kitchen and water is spraying everywhere, knowing how to stop the geyser of water becomes quite important.
Rotate Your Semi-Perishable Food: Canned goods and bottles of water keep well enough, but not forever. Arranging your pantry so that cans don't linger at the back ensures that when you're snowed in you'll be eating fresh canned fruits and vegetables instead of the dusty cans from three Thanksgivings ago. You can go all out and build a rotating shelf to keep your canned goods fresh, but for smaller scale storage a simple wire-frame can dispenser will fit on most pantry shelves.
Keep Batteries and Flashlights on Hand: You'll always want batteries on hand. When it comes to keeping the lights on when the power is out, flashlights are king. Candles are a tragedy waiting to happen. Hundreds of house fires are started every year during power outages as people light up candles en masse to brighten their dark homes. It's 2009, you can buy ultra-efficient LED flashlights for less than the cost of a DVD. Even with the power out there's no excuse for lighting your home with fire.
Have Alternative Heat: If you're preparing for a winter storm you most likely live somewhere with icy winter conditions and deep snow fall. When keeping warm during a winter storm there are two levels of warmth: safe and comfortable. If you're wearing layered clothing and have lots of blankets, 40-50F in your house is safe but not particularly comfortable. Nobody will get frost bite and pipes won't freeze. Comfortable is a personal thing—I'm comfy at 55F, most people prefer at least in the upper 60s—and you'll need to plan accordingly for it. Fireplaces, kerosene space heaters, and other combustion-based sources of heat are less than ideal compared to the efficiency and safety of a central furnace but when operated properly can help keep you warm until power and order are restored.
You absolutely need to make sure that whatever alternative source of heat you plan on using during an outage is clean, operational, and that everyone who will be using it understands how to use it safely. Clean out the chimney before you need it and give that kerosene heater a trial run when you're not under pressure. Unfortunately, unlike swapping candles for LED flashlights, there isn't an ultra modern replacement for ditching combustion-based heat for something fancy. Safety first!
Tools and Materials for Emergency Repairs: You don't need to be ready for a full scale remodeling project but you do need some basics. What if a tree branch falls and breaks a window? In the middle of summer it an annoyance, in the middle of a winter outage it's a giant icy hole to the outside world that will drop the temperature of your home below freezing in a matter of hours. Some heavy duty plastic sheeting and duct tape might not have the insulation value of a triple-pane window but it will keep hot air from drafting right out into your yard.
Communicating from the Winter Wonderland: Phone lines can be damaged by winds and ice, but it is very rare for a winter storm to wipe out the cellular network in an area. Keep your cellphone charged and make sure you have a car charger for it—if the power outage is extended you'll need to top it off at some point. If cellphone service is spotty, you may want to consider sending an SMS message to communicate with friends and family. Often times SMS messages go through just fine when trying to place and actual voice call is sketchy due to weak signal. If you live in the country side you might consider investing in a couple GMRS/FRS hand-held radios with some neighbors. You can pick up a modest but functional walkie-talkie set for around $30.
Stay Well Stocked: If you live in an area where weather can keep you holed up, you need to get into the practice of shopping ahead. When you're buying your regular groceries, purchase a few extra non-perishable things to stock in the pantry. Don't wait to do your grocery shopping until it is critical that you get out that day to do so. The same principle applies to non-food items like batteries, salt and sand for your walk and driveway, and keeping your gas tank full in your car.
Scaling Preparation for Your Situation and Budget: Finally, as we mentioned above, you'll need to scale your level of preparation to your budget and needs. If you can afford it and live in an area with frequent power outages, although a bit pricey, a home generator is a great investment. An apartment dweller that experiences extremely infrequent and brief outages could simply stockpile some batteries under the bed.
The important part in preparing for inclement weather and power outages is to run through potential and reasonable scenarios and what you need to do in various situations that may arise. What if an ice-laden tree falls onto your house? What if the power is out for more than a day? How will I heat food with no electricity? Does the heating system of your home require electricity? Have I told my roommate, spouse, or child what the plan is in the event of an emergency? Asking and answering questions like these well before you're under the stress of the actual situation helps you plan properly and keep stress to a minimum when that Douglas Fir actually does come through the picture window or the guy on the emergency weather radio says power won't be restored until next Tuesday. A small amount of planning now yields a lot of comfort later.