Whether you will be dayhiking or doing a multi-day backpacking trip, these items will insure a safe and enjoyable outdoor experience.
Obtain a map of where you will be hiking. Usually, you can pick one up at the park visitor center or ranger station. You can also download maps from various websites. Having a good map will not only will not only prevent you from getting lost, but it can help rescuers find you if you suffer an injury.
A map reading compass will help you find your bearings and keep you from getting lost. Using the map and compass together will keep you correctly oriented to know which direction you're heading.
Two, one liter bottles of water so that you stay hydrated. This is your minimum required intake per day, but since hiking is physically demanding you will drink more, especially in warmer climates. You can survive for a month without food, but only two or three days without water. You should have some sort of water treatment with you. I carry Aqua-Mira, which is a liquid purifying agent.
Take a bit more food than you think you will need, to get you through an extra day if need be. This can easily be accomplished by having a few whole food bars with you, each of which constitute a complete meal replacement. Important for maintaining energy output.
A few more layers of clothing for comfort and safety. Temperatures can drop unexpectedly or at nightfall. If you hike through rain or fall into a creek, having only one layer of wet clothes when it starts getting colder can spell disaster. Make sure to wear synthetics as they are more insulative when wet and dry quickly.
Bring a small flashlight or headlamp with you. Sunset may occur sooner than expected and you may have a few more miles to go. Hiking in the dark over uneven terrain is dangerous.
Having an accident or injury in the backcountry is no fun. Bring a small first aid kit with you. You can create one out of household supplies but don't forget hiking needs like moleskin or blister treatment. I recommend taking a basic wilderness medicine course.
Matches, a lighter and or candle as firestarters. Be certain to keep them in a waterproof container. Only light a fire in the wilderness if it is a matter of survival, not just simply staying warm if an additional layer of clothing will do. Prevent wildfires, use caution!
Carry a knife with you. Mine has come in handy so many times. If you use a folding knife, make sure that it has a locking blade. Non-locking knives have closed on fingers!
Ultraviolet protection is really important. The suns rays can be damaging to eyes and skin, so bring a good pair of sunglasses, a small tube of sunblock and perhaps a wide brimmed hat.