Specifically for Babies
Milk & Formula Nothing is worse than a hungry baby and no milk, so I pack this thing up with three pre-portioned formula servings, plus I pack a couple of bottles of water. Additionally, I pack two baby bottles loaded up with breastmilk in a lunch box with a couple of ice packs, and all of my pumping equipment, including back-up parts. I leave the pumping equipment in the car, of course.
Carrying the Baby We like this style of baby-carrier for comfort and ease of use.
Breaks Putting the baby down for a break is sometimes awkward as there is no great place for the baby to roam - you don't want the baby to fall into water or crawl through something yucky. I tend to just take a beach blanket and watch the baby closely during breaks.
Specifically for Toddlers
Breaks & Snacks We like to take a break at roughly the halfway point, and eat snacks. We value the ease of the snacks and how much they please the kids over nutritional value on our hikes, so we like sip-ups, fruit snacks, and individual bags of chips. We have picky eaters, but other snack ideas are boxes of raisins or carrot sticks.
Shoes If water is going to be involved, Crocs make life easy. If money were no object, we'd get the kids their own hiking boots, but they're twice as expensive as regular shoes and the kids' feet grow so quickly. So if not Crocs, then we put our kids in tennis shoes or, if they need more grip, then we put them in duck boots since, although expensive, duck boots do double duty as snow boots and can usually be worn when they're one size too big or too small. Whatever you do, don't let your kids wear sandals to go hiking - the sandals will get soggy, or break, or start to rub awkwardly.
Specifically for Elementary School Aged Children
Motivation The fun snacks and the break halfway through definitely help.
Breaks& Snacks Read above under the toddler section as the same holds true for us.
Walking Sticks You can buy a children's walking staff, but honestly you might just be better off choosing a lightweight adult-sized one since it can do double-duty. Use with caution, as you don't want a sword fight to break out.
Shoes Read above under the toddler section as the same holds true for us.