We needed to hire guides for some trails in private reserves, for example, and there can be a safety issue in places. Malaria, hepatitis, and other tropical and third-world diseases can be a concern. We also took chloroquine against malaria. Aside from the children protesting the bitter taste of the chloroquine, we had no problems. We have not tried to keep our travels with children at the shoestring level, but nor do we splurge on upscale hotels or porters at the airport for our mountains of duffel bags.
Gas mileage is appalling, but the remaining costs are minimal.
We always opt for something with a kitchen when possible, and free-standing places such as cottages or cabanas are ideal since we don't need to worry about bothering the neighbors if our children get a little noisy. We've generally found our hosts at such places to be very hospitable, genuinely charmed by our junior travelers. We are willing to pay a little extra to maintain our independence. For example, with small children if it's affordable we'll hire our own boat and guide for a trip upriver in the tropics rather than pile in with 20 adult eco-tourists. Hiking Hiking is an ideal travel activity with small children.