Washington state roadside emergencies can range from a flat tire downtown to being stranded in a snowy ravine for three days. So you may want to consider a basic emergency kit to keep in the car at all times and a travel kit tailored to a specific trip.
Your close-to-home kit for around Gig Harbor would have some basic items to work on your car: everything you need to change a tire, gloves, a couple quarts of oil, some antifreeze and water. A can of tire inflator is a great temporary fix for minor flats. You'll also want jumper cables or a booster box, flares, a flashlight and some basic hand tools.
Now for your comfort and safety: a first aid kit, drinkable water, high calorie food (like energy bars), blankets, toilet paper, cell phone, towel, hat and boots. Keep some change for a pay phone, emergency cash and a credit card.
People who live in areas with frequent severe weather or earthquakes may want to carry provisions for longer emergencies.
For trips away from home, consider the weather and geography as you assemble your emergency supplies. You'll need to have a source of light and heat and will want to provide protection against the elements as well as adequate food and water for everyone in the car.
Always tell people where you are going and have a plan for checking in at way points. Then if you run into trouble, you can be reported missing as soon as possible and rescuers will be able to narrow the search area.
The key to safe travel is to keep your vehicle properly maintained, plan ahead, and let others know your itinerary.