Trees crop up in many different contexts, including computer science: if a computer programme makes a yes/no decision at every step of some process, then its combined options can be presented as a binary tree (see figure 2). Another example is genetics, where trees are used to describe the evolution of species. This context has actually produced some some very hard (though not undecidable) mathematical questions (see thePlus article Reconstructing the tree of life). So in terms of concrete incompleteness, trees are a good place to look.