Honesty is a quality that all companies are looking for in prospective employees.
If you can't be trusted, then you probably are unemployable. However, it is fair to say that any role that involves the handling of money demands that the person be honest.
I always find it fairly disheartening when I hear of a case of someone who stole money from the company they worked for.
It is even worse when you are the one being stolen from. I have been a victim of such theft before and I can assure you that the sense of betrayal is huge. What made it worse is that I had trusted the person. I think the betrayal of trust is often the biggest issue - more so than the actual amount stolen (depending on how much, of course. In my case it was a relatively small amount).
It is not only people who handle money who can be tempted in this way, but also those providing a service, like courier drivers.
