How And When Should You Report Co-workers?

Well, if they are stealing, then I would report them. If they are not doing their job, causing others to have to work harder as a result, or just screwing things up in general, then I would report someone. Other then that, I do not know

If you now that they are doing something that isn't right. Do you have an ethics hot-line? If so call it.

When you observe them doing something unethical or if the person is making you feel uncomfortable by making advances at you, bullying you,threatening you , go to your Human resources office

It depends on what you want to report them for.  However, I believe that you should always approach the person directly first, to give them a chance to rectify their actions.  If they do not listen or try to improve, then it is just a matter of finding their direct superior or supervisor/manager and make the report to them because that's their job to look after those below them.