There are 2 kinds of packers. Light packers, who bring only what they absolutely need and heavy packers...like me, who bring everything the could POSSIBLY need, just in case of an emergency or some sort of natural disaster.
So as a heavy packer, I tend to buy big bags. This is an ORE day tripper by Sugarbooger. As the name suggests this is my day trip bag. In the center part that zips I have 3 loaded FLIP covers (loaded with disposable inserts for this particular trip) and 3 extra inserts. If you have a frequent pooper, I suggest bringing more covers. My "rule" is 1 diaper per hour we'll be gone plus one extra.
I use disposable wipes when out and about. I bring a small wetbag in case one of the covers gets soiled. These and my "personal" bag go in the center.
In my personal bag, I have my wallet, ipod, chapstick, lotion...anything I'd need if I was going somewhere sans kids. The ladybug is a small flashlight that doubles as a toy if someone gets cranky. I also keep a small camera w/ me all the time in case the kids do something funny I want to capture.
In this particular bag, there are 2 side pockets. In 1 pocket, my HUGE Nalgene water bottle lives. As a nursing mother, I drink a LOT of water. My nursing cover rolls up and fits next to it. Bonus is if the water is cold it makes the cover cool, which is wonderful on a hot day.
And the other side has all my random stuff...a reusable shopping bag, a package of bandaids, neosporin, tweezers and safety pins, handwipes, sunscreen and something sugary to feed my 4 year old when she gets cranky. I often bring a small baggie of nuts or a granola bar for me since I tend to get really hungry while nursing.
All packed up:
For a short trip to the store, I'd pack a smaller bag with 1 or 2 diapers, a small wetbag, wipes and then throw my wallet and phone in there somewhere.
This is a Land's End Little tripper with 2 bumgenius organics, a small pack of wipes and a wetbag
One other option is to pack a bag and leave it in the car. I bought this little cheap bag off Amazon for less than $10. It could easily fit several prefolds and a package of inexpensive Dappi covers, a change of clothing for baby, wipes etc. The only drawback to this idea is that those diapers aren't in rotation and can be outgrown before they are worn much.