Before you leave make sure some know where you are going and how long you will be gone. If plans change make sure you notify that person
Never hike alone
Be prepared, think about what gear, clothing, food, water, etc you may need and what you will need if something bad happens. Don't go over kill as hauling a ton of gear is no fun either.
Check with local authorities, ranges, etc to see if you need permits, maybe the trail has been washed out, is closed for maintenance, or maybe you will find out the trail is more difficult then you thought. They can even warn you about possible weather and animal issues.
If you plan to bring a dog along, make sure you know the rules, for example National Parks do not allow pets on trails any more.
Take only photographs, leave only footprints, kill only time
It is a good idea to stay some what together as a group for safety reasons, but also stay spread out enough to reduce your impact on the environment you are walking through and the animals you may see.
When you come to switch backs, for example where the trail may zig-zag up the side of a hill side, also follow the trail. Cutting the switch back is not only harder physically, but causes a variety of damage to the trail and environment such as erosion.
Always leave it cleaner then you found it. Pick up trash and pack it out. Pack it in, pack it out.
When passing fellow hikers, step to the right (if possible) and remain calm
When you meet horses or mules on the trail, also step off the trail or all have everyone as far to one edge of the trail as possible. Remain quiet as noise and movement may spook the animals.
If you come across a gate, leave them as you found them. If it is closed, then close it behind yourself, if it is open leave it open.
Use Peaceful and Quiet Voices
Stay on the trail at all times
If you are hiking through a muddy mess, stay on the trail as well, if there is no evidence of a trail find a safe route through
Avoid sensitive areas that include wetlands, streams, meadows, forest, desert, lake shore and, breeding or nesting areas. Avoid sensitive soil areas to prevent damage including erosion.
If you run out of trail, do not cut a new trail, this will cause more damage and erosion. Instead fan out, try not to walk single file, this will lessen the impact on the area.
Stay away from private property, you must obtain permission from the land owner prior to hiking or you will be trespassing and trespassing is punishable by law.
Avoid spooking wildlife and livestock, keep a safe distance to avoid attacks.
If you notice damage to the trail, signs, etc make sure you take note and notify the proper authorities such as park rangers.
I hope you found this list useful. Please feel free to tell us stories of your hikes, rules I may have missed, etc in the comments section below.