Car engines today are based on the principle of burning fuel to create energy in the form of motion. But if our society was limited to materials like wood or stone, modern engines would simply not be possible. We would still be riding wooden bicycles and using canoes. This last point is particularly important. Since motorized travel will be impossible, water will be the most convenient and most efficient way to travel. Indeed, much of civilization would have congregated around bodies of water.
But we would still be able to accomplish much more than one might initially think. It is possible to carve gears and levers with a stone knife or something similar, allowing for construction of complicated machinery. Indeed, in a world where human civilization continued developing without the discovery of metal, we might be living in a "woodpunk" (taken after the word "steampunk") world -- with complicated wooden machinery buzzing all around us.
Returning to our starting point, look around you: metal everywhere. Without metal, we can accomplish so much yet so little. Indeed, removing such a staple in our life forces us to thing hard about living in a new situation, even a new planet in the future. So what other possibilities and impossibilities can you imagine in a world with no metal?