Battery Operated Lanterns
Battery powered lanterns provide good light for most rooms. They will provide light for several days. However most of them take a lot of batteries, so you cannot depend on them for long term use unless you have a lot of battery storage. Battery powered lanterns are a safe and effective way of lighting a room on a temporary basis.
Propane LanternsPropane lanterns work well, but they use a lot of propane so you can't count on them for long term storage unless you have a lot of propane.
You will need flashlights to walk around your home when it gets dark. Store batteries, but be sure and rotate them so they don't get old. Batteries leak so do not store them in your flashlights.
Also available are flashlight that light after you wind or shake them. The light lasts for a couple minutes.
If you want task light a head lamp comes in handy. Head lamps last up to 30 hours and are powered by LED lights.
Everyone has candles. Along with solar power they are a good long term solution for light. You can purchase candles made for emergencies that will burn for up to 100 hours. Just be sure you have a holder for them so they won't fall over and start a fire. Candles are almost always the cause of home fires during power outages, so be very careful. You also need to store matches. Keep them stored in a container where they won't get wet.
Light sticks are a great resource. They will give your many hours of light.
Solar LightsSolar Lights are wonderful. Place solar lights in your yard during the day and then bring them inside during the evening. Check out the Luci light. Is is an inflatable solar light that is easy to transport. During the winter, you will also have light from fireplaces and wood burning stoves.