Those you have to run from and those you can sit tight for.
You have to run from wild fires, floods and large hurricanes. You can sit out blizzards, small hurricanes and the like.
Okay, there are plenty like tornados and earthquakes that are come as you are, and you figure out afterwards if you have to leave or can stay, depending on damage to your home.
So what do you do to get ready?
You need a couple of kits: An evacuation kit and a shelter in place kit.
An Evacuation Kit is a 72 hour kit optimized for getting out of Dodge.
A couple of liters of water and some lightweight food, I like GORP myself as that has plenty to energy to keep you going for 3 days.
A simple first aid kit, just bandaids and some elestic wrap. Good for a cut or sprained ankle.
A good map to get you to your evacuation point.
A multitool and flashlight.
And copies of important papers.
A Shelter in Place kit can be much bulkier as it and you aren't going anywhere.
2 weeks of food and water. This can be regualr stuff you eat preferably canned as it doesn't need to be kept cool and about 14 gallons of water per person.
A battery operated radio but you can use the one if the car.
A tool kit to repair the house if it gets damaged.
You can add plastic sheeting and duct tape, but don't forget to cover the furnace intake vents and all the other vents into your home.
An extensive first aid kit.
Flashlights and extra batteries. Candles and matches but be careful and don't burn your house down.
This is just and overview. I'll be fleshing this stuff out over time.