When I had my first kid, I carried everything-but-the-kitchen-sink in my diaper bag. I was prepared for any kid emergency. And I never used half of the things that I carried. This was torture for a gal like myself, who prefers to travel light.
So, now that I'm older and wiser and more experienced, here's my EveryDay Carry (EDC):
On Person: Folder Knife (2.5 inch blade, nice and sharp)
On Keys: Small Swiss Army Knife, small LED flashlight
In Purse: Wallet, small LED flashlight, penknife, pen, paper, epi-pen (for allergies), chapstick, hairband, feminine supplies, BIC lighter, 2-3 diapers and pack of travel baby wipes
In Diaper Bag: 2-3 diapers for both kids, travel package of wipes, receiving blanket, pants for each kid (in case of accidents), sling, lollipops (I will sometimes throw a sippy cup or snack into this bag, too.)
If need be, I can grab just my purse and leave the house with the basics I need for a 4-5 hour outing with my kids, although I usually bring the diaper bag with me for extended errands.