When youre hiking uphill, especially with a backpack, take short steps, keeping your weight even. Dont lean into the hill too far, especially on wet terrain - you will slip forward. Likewise, when going downhill dont get in the back seat or you will find yourself on your seat.
Keep your boot or trail shoe laces in tight loops. Boots and trail running shoes tend to have long laces. If you tie them and leave a big loop, your shoelace loop will find a root or something else to catch on and could start a nasty fall. So back lace down your boots or otherwise shorten your laces to keep them tight.
Wear gloves. Short finger biking gloves are good, but you can use any kind that keep your palms from getting blisters from the pole handles and will aid in climbing.
Buy a small First Aid kit, a small flashlight and a multi-purpose tool like a Swiss Army knife.
Carry a small roll of duct tape, the universal fix anything.
Dress for the days weather, but be prepared for whatever possible weather your area can throw at you.
Be sure your cell phone has at least some service in the terrain you will be in.
Carry a topographical map and know how to read it and how to use a compass.
Think about investing in a GPS for your hiking. Its a great gadget to have and to insure your safety.