I have three children, ages 5-9, and I'm a "be prepared" kind of mom. I find that one of the ways to effectuate always being prepared is to keep some essential items in my car at all times. There is nothing I can't effectively handle with these things at my disposal.
Towels: I keep a small stack of beach towels in the cargo area of my minivan, and I have used them many times over. Turns out I have kind of pukey kids, mostly due to their gastric reactions to food allergies. But towels come in handy in all sorts of situations, not just when a child strapped in a car seat throws up. Though particularly useful for clean-up and cover up during those times, having extra towels in the car is also handy for dealing with the aftermath of potty accidents, getting caught in the rain, a muddy playground encounter, and general food and drink related disasters. I've also used them to dry early morning dew off a playground slide. And even as a seat cover for myself after a particularly sweaty run or visit to the gym.
Change of Clothes for EVERYONE: Any manner of issues necessitate changing your kids' clothes, most of which involve one of those above-mentioned handy towels for clean-up first. And for a long time I just kept a full change of clothes in the car for each of the kids. Until the day that my then not quite two year old started to throw up in a restaurant, so I grabbed him up, clutching his face to my chest, as I bolted for the door. That was the day I learned that I needed to also keep a change of clothes in the car for myself. That was one unpleasant drive home, one I spent wishing I had the foresight to keep a clean t-shirt for myself in the car.
Extra Pair of Children's Shoes: Another one I learned the hard way when after a 30 minute drive from our home to our destination my 8 year old son announced that he had forgotten his shoes! Luckily our destination was near a department store, but I grumbled mightily as I shelled out for new shoes because of his oversight. Now I keep a pair of flip-flops in a size worn by my middle child in the car. Flip-flops are a great option for this extra pair of shoes because they're still usable if they're a little bit too small or too big. And guess what? Each of my children has worn this extra pair of shoes at least once in the past year. Apparently only the last half of the "put on your shoes and get in the car" command reaches their ears.
Plastic Bags: These have been a life-saver on many occasions for many different reasons. I personally prefer to keep several gallon-sized Ziploc-style bags handy because they are made of a durable plastic and can be securely zipped shut. But grocery store plastic bags are also handy when you just need a garbage bag or a larger bag capable of handling some dampness. I've used them for improvised barf bags, to keep muddy cleats off my car interior, to hold wet bathing suits from the pool and beach, to clean trash from the back seat, for wet clothes after potty related incidents, for various "treasures" acquired from nature walks or the beach, and the list goes on and on.
Snacks: This is a big one for me, especially since my children have food allergies, but I consider keeping a few non-perishable snacks in the car both a time and money saver. How many times have you gone somewhere with your kids only to have the adventure last much longer than you thought it would? I like being able to dole out some sustenance without having to get everyone out of the car and into a store. I also enjoy having something like almonds for myself to munch on during a busy day of running around, or when I forgot to pack my own lunch and don't feel like eating out.
Those are just a few things I keep in the car to handle all manner of kid-related situations. These few essential items have averted disaster and kept us on track many a time.