In which situations would I use a red/black tree instead of an unbalanced tree?
Red-Black trees are a form of balanced trees. This means that the tree height is always O(log n), where n is the number of node in the tree. The effect of this is that searching for a node in a balanced tree takes O(log n) time. Similarly, adding and removing also take O(log n). This is in contrast to unbalanced trees, where the worst-case complexity for searching/adding/removing is O(n) (which means that in the worst case they're not any better than linked lists).
You should use balanced trees whenever you need to bound the worst-case performance of operations on the tree.