At some point we picked up a cheap first aid kit at the drugstore and thought "done," but when we read a list of suggested items for one at Unclutterer we realized ours was woefully inadequate even with all the other junk filling up our medicine cabinet.
The Unclutterer post was written by a professional organizer, Geralin Thomas, so you can bet she's got all the bases covered. In addition to a pretty comprehensive list of items to have on hand either in a kit or quickly accessible in your medicine cabinet, she suggests keeping an index card with the home address and cell phone numbers of the parents (in case you get flustered on the phone), children's names, birthdates and any allergies, and contact information for your pediatrician and pharmacy.
See the full list here. And remember, the best time to put together a first aid kit is before you need it.
(p.s. Have you put together your Emergency Preparedness Kit yet?)