I am a real fan of making your own survival kit. This is the essence of self-reliance and with this approach, you know what's going into your kit, how it works, and that it is tailored to fit you. Your kit should contain items to take care of the "Big 5" survival priorities: Shelter, Water, Firemaking, Signaling, and First-Aid.
For a guideline, here's what I carry:
Blue tarp (5x7 blue poly-tarp)
-Remember that your first shelter is your clothing so dress appropriately (i.e., no cotton, but fleece or wool)
Potable Aqua Iodine or Chlorine Dioxide Tablets
REI StormProof Matches
Cottonballs smeared with Vaseline (as a wet weather firestarter) stowed in a film canister
2"x 3" glass signal mirror
PLB (Personal Location Beacon) if I am going on a remote trip
One person First-Aid Kit by Adventure Medical Kits with a few goodies added like Fast-Melt Benadryl for bites, Ibuprofen, Immodium, an ACE wrap, and duct tape.
Swedish Mora Knife
Leatherman or Swiss Army Knife
I carry some of my gear in my pockets (firestarters mostly) and the rest in my fanny pack.
I like eating well in the backcountry, and while food is not an immediate survival priority, I like to be prepared and have jerky and some Clif bars with me.
If my kids are on the hike with me, then they each have their own mini-kit consisting of a large orange trash bag for shelter (poke a hole in one corner to form the hood), a whistle, water bottle, snacks, and appropriate clothing. As they get older, they will get some of the above gear I carry.
Now, if you don't want to fashion your own kit, then consider buying one of the quality kits made by Adventure Medical Kits or OutdoorSafe.
With either a homemade or store-bought kit, just make certain that you test out the items before heading out on the trail and to obtain quality gear- this is your life insurance!
Lastly, tell someone where you are going and when you will return. This is your safety net working for you on the other end and can help prevent you from ever having to crack open your survival kit in the first place.