Angela, the question is biased. What is the definition of "overuse"?
Some resources are renewable, and by using them at a rate greater than they can be renewed we deplete them. In the case of animals or fish, we can drive a species to extinction or cause major changes to an ecosystem if, for example, we kill all of the natural predators or a key food supply in the food chain.
Ecosystems can also be treated as "natural resources". By consuming old-growth forests, wetlands, and natural habitats and by flooding land for hydroelectric projects we can cause the extinction of species that rely upon these habitats. Some of the other side effects can include long term climate changes or irreversible erosion of topsoil.
Some resources are not renewable - such as mineral deposits, petrochemicals and the like. Whether you use them quickly or whether you use them slowly, they don't come back. For this very reason it is hard to define "overuse", since any use at all will have the same effect - depletion of the resource. THat does not mean that we should not use these resources - just that we need to bear in mind that we will not be able to do so forever, and need to keep looking at "what's next". Problems arise when we fail to see the train coming and become so dependent upon a particular resource that we become desperate as its supply diminishes. Under such circumstances we end up doing things that we would not otherwise do - both to the environment and to each other. We need to make sure that we never force ourselves into the position of doing stupid things out of desperation. That in my mind would constutute "overuse" of a non-renewable resource.
As far as human impact is concerned, nature is remarkably capable of cleaning itself up. I would say that the self-cleaning ability of the earth's ecosystems is one of the most important natural resources that we have. If you drop dead in the jungle, within a few months there will be hardly a trace of you. If you burn hydrocarbons, a tree will be happy to convert the carbon dioxide into wood, or a marine animal will be happy to convert it into a carbonate shell. However, if you overwhelm the rate at which nature can balance itself, you can cause problems. The key is not to say "don't pollute". Any animal that takes a dump in the woods is polluting. The key rather is to not pollute faster than natural processes can remediate the pollution. This goes for anything from acid rain or acid mine drainage to chemicals to carbon dioxide. If you pollute faster than the earth can clean itself up, you are overusing the earth's natural ability to rebound.
So how quickly can nature remediate pollution? Nature has really good mechanisms for dealing with some things, but virtually no mechanism for dealing with others. It is the things for which nature has no mechanisms that pose the dangers - substances such as chlorofluorocarbons (CFC's) or polychlorinated biphenols (PCB's), or DDT, dioxin, or any one of a number of other problematic substances. There are some man made substances against which nature is so defenceless that virtually any discharge of them constitutes overuse of the environment's ability to rebound.
The world has an equilibrium, and our use of natural resources shifts this equilibrium. This is not a bad thing in and of itself - we humans are part of nature, too. Your own home town, wherever that may be, is probably there because at some point in the past it offered a resource that was valuable. The only thing that we need to watch is that we do not push environmental equilibria past the point of no return, and cause irreversible consequences such as extinctions and entire loss of ecosystems that we did not originally intend.