There are many thoughts on what to bring on a hike. Since I am not into being too adventurous and I never go off trail I don't bring maps and compasses or anything too technical. However these items are a good idea if you plan to go off trail.
Here is a list of things I bring on a hike with my kids. I always fit everything into my backpack.
1. Layers: Like I mentioned in one of my posts, the temperature and weather can change quickly due to the elevation gain on hikes so I always bring a jacket for everyone in my hiking party.
2. Water: This is a necessity on any hike. I bring about 32oz. per person depending on the length of the hike. If you plan to do multiple hikes, I would invest in a Camelbak type of device for each child so they can be in charge of their own water. This saves you having to lug around everyone's water and having to listen to "mom, I'm thirsty" the whole way :)
3. Food: I usually pack a lunch and some snacks to eat along the way. Kids will always be hungry and a snack/lunch can be a good motivator to make it to the top. They also need energy since hiking can be tiring.
4. First Aid kit: I pack mine with pain reliever, band aids, antibacterial ointment, wipes, gauze, anti-diarrhea medication, allergy meds, hand sanitizer, matches, and anything else child-specific you may need. (Ex.epi-pen or inhaler). Garbage bags are also easy to store and make great rain gear in an emergency.
5. Multi-tool: For example a Leatherman tool just in case you need it.
6. Sunscreen and bug repellent: You can get individually wrapped packs of sunscreen and bug repellent that will fit easily in your backpack. You can also get bug fans that clip to your belt or bug bracelets. I haven't tried these products yet, but plan to try them all and report on how well each one works.
7. Small Flashlight: I would bring extra batteries too just in case. Although I don't hike at night, it is always a good idea to carry a flashlight if only to peer into logs etc. for curious eyes.
8. Biodegradable toilet paper (self explanatory)
9. Cell phone: This is a must in case of emergency. Make sure it is fully charged when you begin your hike. I also use mine to take all of our pictures. It actually takes better pictures than my camera and gives me one less thing to carry.
10. I always bring my driver's license and insurance card. This ensures that if there is an emergency all parties will know who I am and have my medical information. I also have a Road ID that velcros to my shoe. I originally purchased this because I am a runner and it is a useful tool in case of emergency, but it works great for hiking too. It includes whatever information you want such as name, emergency numbers, health info etc. You can go to www.roadid.com to learn more.
Finally, I carry a whistle and pepper spray (in case of animals or weirdos). Make sure you know how to use the pepper spray before you begin your hike. The time to read the directions is not when an angry animal is rushing towards you.