Would it be considered unethical to anonymously report my suspicion that several co-workers are stealing from customers and the company I work for by suggesting the company conduct an investigation into the practices of their employees to determine whether or not this is actually occurring? I ask this because I highly suspect this is the case where I work. Should I simply turn a blind eye? My internal conflict regarding this situation is that almost no one likes the company and the clientele they work for, which is in part, why I believe some employees feel they are justified in indulging their greed by stealing from both company & client. I mention 'greed' because I suppose this is why I feel compelled to report my suspicions. So many of my co-workers behave abusively to one another because of their greed and I suppose I feel that these nasty, greedy individuals deserve to be called on their unethical behaviour, but once again, I wonder if it is up to me to be the one to see to it that they receive...

As far as I can tell from your description, it would not be unethical to report such fraud--indeed, reporting it is likely the right thing to do. Depending on the details, it might even be illegal not to report it. You might want to consult a legal expert to determine your rights and responsibilities in this case. It sounds like you are in a bad company and a bad situation. I wish you the best as you try to make things better.

What does a person do when his or her co-workers do not do their job and he or she is always doing their job?

Stop. Let their ineptitude and laziness shine forth in all it's glory. Hope they will be replaced by people who do their own work as effectively as you do. If this fails, try to ensure that higher-ups know what you are doing so you are compensated more appropriately.