Farmer and the boat
Probably the best known example of a crossing puzzle. Good warm up to something more complicated like cannibals and missionaries.
A farmer is traveling to the market with a wolf, a goat, and a head of cabbage, when he comes to a river. The only way across the river is on a small boat, which can carry only the farmer plus one of his three items at a time. Complicating matters is the fact that if the farmer leaves the wolf and goat alone on either side of the river, the wolf will eat the goat. Similarly, the goat will eat the cabbage if the goat is left alone with the cabbage on either side of the river. How can the farmer get his goods across the river safely?