An emergency kit is more than just a first aid kit.  It is also a repair kit and survival kit.

Include survival items should you become stranded overnight.

Everything should be in a waterproof container or Ziploc bag.

Using a small fanny pack lets you grab it and go.

Emergency items:
    Spare flashlight
    Tea candles
    Spare lighter
    Spare whistle
    Fire starter
    Army can opener
    Pocket poncho
    33 gallon trash bag (climb in feet first - with a poncho it provides emergency shelter)
    Pocket mirror
    Pocket knife

Repair items:
    Glue
    Parachute cord
    Duct tape or electrical tape
    Sewing kit
    Eyewear repair kit
    Safety pins (assorted sizes)

First aid supplies:
    Snake bite kit
    Tweezers
    Tick remover
    Alcohol swabs
    Neosporin (triple antibiotic ointment)
    Hydrocortisone ointment
    Colgate toothpaste (travel size - apply to insect bites)
    Benadryl (diphenhydramine) tablets/capsules (for allergies and insect bite reactions)
    Pain reliever
    Moleskin
    Ace bandage
    Band-aids
    Gauze bandages
    Bandage tape
    Bandage scissors
    Soap (hotel size)
    Q-tips
    Eye cup
    Ear syringe

This gear list reflects what we personally carry.  Other equally experienced hikers might have items to add or subtract from their lists.  Ultimately, you will find what works for you.  We make no claim as to the completeness of this list, nor is it intended to substitute for adequate skill training.