This could go either way. It could either get in your way if you get into a sticky spot, or it could assist you if you just don't have enough traction. I do not personally walk with one, but I know someone who does. She uses it as a brace just in case she loses her footing, and uses it as a tripod for her Canon EOS Rebel (she is very into photography, which is the main reason she joins us on many of our hikes). If you will be walking anywhere with loose footing, such as on shale, gravel, ice, or snow, I would recommend bringing along a walking stick, as they can assist getting that little bit of extra traction needed. The one my friend uses that seems to be a very good, lightweight walking stick with a rubber grommet covered planting spike, a compass on top, and a removable cap with a screw for her camera underneath is the Adjustable Aluminum Trekking Pole. If you are not going to be on one of these surfaces, I would not personally bring one unless I needed it for a camera mount.
One piece of equipment you should never be without. I used to lug Nalgene bottles up with be, which really do not carry all that much water, and can be rather awkward to hold unless you put them in a backpack. If you are going to put it in a backpack anyways, might as well invest in a good hydration pack. They typically hold a liter or more of water, and can keep that water cold for a long time due to the insulation in the pack (even better if you add ice). That extra water may be important if you get lost, or someone gets hurt and you are stuck on the trail for longer than expected. I like the Camelback M.U.L.E., because it can hold up to 100 oz. of water, and the pack has compartments for all kinds of other gear, so you can bring along your camera or food or something and keep your gear somewhere easy to carry and relatively safe.
Most people overlook this item. Socks can make the difference between a good day and a bad day. If you are going over a few miles in distance, especially if you are changing elevation quite a bit, it is a good idea to wear a pair of good padded wool hiking socks. These will pad your feet on the areas that see the most impact, as well as offering some protection against blisters. If wool bothers your skin, thin sock liners are made to wear with them.
If you are bringing a pack in the first place, you might as well have everybody bring an extra pair of clean dry socks just in case. You will thank yourself if you lose your footing and step in water.
See above explanation.
Always always ALWAYS wear sunscreen if you are going hiking. It will protect your skin from the harmful, cancer causing rays of the sun, and probably prevent a painful sunburn.Always wear it, even if it is cloudy. Always. What part of always don't you understand?
I could go either way on this. I always lose sunglasses, and hats bug me when I'm wearing them, so a lot of the time, I will try to wear them, but they end up in my backpack. They are a good idea to bring, in case it is really bright out to help you see past the bright, reflective soil for footing (or dangers). If you buy sunglasses, make sure they are polarized, otherwise you are pretty much wasting your money.
First Aid Kit/Survival Kit:
This is just dumb not to bring. Things happen when you get out and active. Follow the Boy Scout's motto: Be Prepared. This kit may end up saving your life if you get injured and stuck somewhere more remote than the mountains of Los Angeles, as (depending on the contents) it may give you the emergency blanket and matches to build a fire and keep you warm through the night or until help can arrive.
You can bring a compass if you know how to use one. I'm not going to say they are not useful, because they are very useful, but most people (especially in the mountains around Los Angeles) would have more luck if they get lost just following geographic features. Canyons are there because they are where the water runs during a rainstorm. They always converge, and when they do, eventually, they will lead to the watershed. In the mountains around LA, if you get lost, you can always follow a canyon (waterbed) until you get back to a recognizable area. From there, you can get back to civilization. Just be sure to watch out for cliffs, and be extra careful not to get yourself injured in the process of making your way out. Remember, this is always a possibility if you leave a marked trail, or are trailblazing; hike at your own risk.
Since you have your pack anyways, make sure to pack some snacks/food. Either a good lunch, or some granola, trail mix, dried fruit, or beef jerky will do the trick. This is more of a convenience item, in case someone gets hungry (unless, again, someone gets themselves lost, in which case he would be thankful to have this).
This is one things that I always bring with me. With a couple of holes torn into them, they can serve as a poncho in case rain surprises you, they can serve as a pretty good emergency blanket in a pinch, or if you are just going for a short hike, you can use them to do an impromptu trail cleanup, picking up trash as you hike, and chucking it on your way out. A lot of the trails in Los Angeles see heavy use, and many people do not do their part to keep them clean. The rest of us suffer. The more of us that work to keep our trails clean, the better they will be, and the easier it will be on each of us.